Relevant bibliographies by topics / General theory of categories and functors

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'General theory of categories and functors'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "General theory of categories and functors"

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Morrison, Scott, and David Penneys. "Monoidal Categories Enriched in Braided Monoidal Categories." International Mathematics Research Notices 2019, no. 11 (2017): 3527–79. http://dx.doi.org/10.1093/imrn/rnx217.

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Abstract We introduce the notion of a monoidal category enriched in a braided monoidal category $\mathcal{V}$. We set up the basic theory, and prove a classification result in terms of braided oplax monoidal functors to the Drinfeld centre of some monoidal category $\mathcal{T}$. Even the basic theory is interesting; it shares many characteristics with the theory of monoidal categories enriched in a symmetric monoidal category, but lacks some features. Of particular note, there is no cartesian product of braided-enriched categories, and the natural transformations do not form a 2-category, but
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Hoofman, Raymond. "The theory of semi-functors." Mathematical Structures in Computer Science 3, no. 1 (1993): 93–128. http://dx.doi.org/10.1017/s096012950000013x.

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The notion ofsemi-functorwas introduced in Hayashi (1985) in order to make possible a category-theoretical characterization of models of the non-extensional typed lambda calculus. Motivated by the further use of semi-functors in Martini (1987), Jacobs (1991) and Hoofman (1992a), (1992b) and (1992c), we consider the general theory of semi-functors in this paper. It turns out that the notion ofsemi natural transformationplays an important part in this theory, and that various categorical notions involving semi-functors can be viewed as 2-categorical notions in the 2-category of categories, semi-
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CISINSKI, DENIS–CHARLES. "Locally constant functors." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 3 (2009): 593–614. http://dx.doi.org/10.1017/s030500410900262x.

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AbstractWe study locally constant coefficients. We first study the theory of homotopy Kan extensions with locally constant coefficients in model categories, and explain how it characterizes the homotopy theory of small categories. We explain how to interpret this in terms of left Bousfield localization of categories of diagrams with values in a combinatorial model category. Finally, we explain how the theory of homotopy Kan extensions in derivators can be used to understand locally constant functors.
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Jay, C. B. "Lambek's operational categories." Bulletin of the Australian Mathematical Society 33, no. 2 (1986): 161–75. http://dx.doi.org/10.1017/s0004972700003038.

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An operational category is a category of models for an equational theory where the interpretation of some operations is predetermined. Examples include the equational and co-equational categories of Linton, categories of functors preserving some class of limits, and algebras for a prop as defined by MacLane. The chief result is a characterisation of the operational categories and functors in terms of their internal structure.
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WISBAUER, ROBERT. "LIFTING THEOREMS FOR TENSOR FUNCTORS ON MODULE CATEGORIES." Journal of Algebra and Its Applications 10, no. 01 (2011): 129–55. http://dx.doi.org/10.1142/s0219498811004471.

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Any (co)ring R is an endofunctor with (co)multiplication on the category of abelian groups. These notions were generalized to monads and comonads on arbitrary categories. Starting around 1970 with papers by Beck, Barr and others a rich theory of the interplay between such endofunctors was elaborated based on distributive laws between them and Applegate's lifting theorem of functors between categories to related (co)module categories. Curiously enough some of these results were not noticed by researchers in module theory and thus notions like entwining structures and smash products between alge
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Neeman, Amnon. "$K$-theory for triangulated categories I(A): Homological functors." Asian Journal of Mathematics 1, no. 2 (1997): 330–417. http://dx.doi.org/10.4310/ajm.1997.v1.n2.a9.

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Neeman, Amnon. "$K$-theory for triangulated categories I(B): Homological functors." Asian Journal of Mathematics 1, no. 3 (1997): 435–529. http://dx.doi.org/10.4310/ajm.1997.v1.n3.a3.

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Cox, Ben. "-Categories and -Functors in the Representation Theory of Lie Algebras." Transactions of the American Mathematical Society 343, no. 1 (1994): 433. http://dx.doi.org/10.2307/2154540.

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Pestov, Vladimir G. "Universal arrows to forgetful functors from categories of topological algebra." Bulletin of the Australian Mathematical Society 48, no. 2 (1993): 209–49. http://dx.doi.org/10.1017/s0004972700015665.

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We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on the relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and other may become amenable to the methods of this theory.
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Buss, Alcides, Siegfried Echterhoff, and Rufus Willett. "Exotic crossed products and the Baum–Connes conjecture." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 740 (2018): 111–59. http://dx.doi.org/10.1515/crelle-2015-0061.

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Abstract We study general properties of exotic crossed-product functors and characterise those which extend to functors on equivariant C^{*} -algebra categories based on correspondences. We show that every such functor allows the construction of a descent in K K-theory and we use this to show that all crossed products by correspondence functors of K-amenable groups are K K-equivalent. We also show that for second countable groups the minimal exact Morita compatible crossed-product functor used in the new formulation of the Baum–Connes conjecture by Baum, Guentner and Willett ([‘Expanders, exac
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Dissertations / Theses on the topic "General theory of categories and functors"

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Al, Hwaeer Hassan Jiad Suadi. "Grothendieck categories of enriched functors." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42873.

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Panchadcharam, Elango. "Categories of Mackey functors." Doctoral thesis, Electronic version, 2007. http://hdl.handle.net/1959.14/119.

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Thesis by publication.<br>Thesis (PhD)--Macquarie University (Division of Information & Communication Sciences, Dept. of Mathematics), 2007.<br>Bibliography: p. 119-123.<br>Introduction -- Mackey functors on compact closed categories -- Lax braidings and the lax centre -- On centres and lax centres for promonoidal catagories -- Pullback and finite coproduct preserving functors between categories of permutation representations -- Conclusion.<br>This thesis studies the theory of Mackey functors as an application of enriched category theory and highlights the notions of lax braiding and lax centr
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Lockridge, Keir H. "The generating hypothesis in general stable homotopy categories /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5817.

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McSween, Alexandra. "Affine Oriented Frobenius Brauer Categories and General Linear Lie Superalgebras." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42342.

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To any Frobenius superalgebra A we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer categeory. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras gl_m|n(A) with entries in A. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where A is the ground field and the two-dimensional Clifford superalgebra, respectively. We include background on monoidal supercategories and Frobenius superalgebras and disc
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McBride, Aaron. "Grothendieck Group Decategorifications and Derived Abelian Categories." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/33000.

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The Grothendieck group is an interesting invariant of an exact category. It induces a decategorication from the category of essentially small exact categories (whose morphisms are exact functors) to the category of abelian groups. Similarly, the triangulated Grothendieck group induces a decategorication from the category of essentially small triangulated categories (whose morphisms are triangulated functors) to the category of abelian groups. In the case of an essentially small abelian category, its Grothendieck group and the triangulated Grothendieck group of its bounded derived category are
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Kerkhoff, Sebastian. "A General Galois Theory for Operations and Relations in Arbitrary Categories." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-73920.

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In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic proper
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Erol, Korkmaz Habibe Tugba. "The Relationship Of Categories Of Work Events To Affective States And Attitudes In The Workplace: A Test Of The Affective Events Theory." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611583/index.pdf.

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Affective Events Theory (AET) of Weiss and Cropanzano (1996) provides a theoretical basis for explaining the antecedents and consequences of affective states at work. In this study, an extended model based on the AET framework was tested for examining the relationships between work events, affective dispositions, affective states and reactions, and the work attitudes and behaviors of the employees. Work events were assessed comprehensively using an affective work events inventory developed as part of the study. A tripartite affect structure (pleasure, calmness, and energy) was adopted for mapp
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Blanc, Anthony. "Invariants topologiques des espaces non-commutatifs." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2013. http://tel.archives-ouvertes.fr/tel-01012109.

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Dans cette thèse, on donne une définition de la K-théorie topologique des espaces non-commutatifs de Kontsevich (c'est-à-dire des dg-catégories) définis sur les nombres complexes. L'introduction de ce nouvel invariant initie la recherche des invariants de nature topologique des espaces non-commutatifs, comme "simplifications" des invariants algébriques (K-théorie algébrique, homologie cyclique, périodique comme étudiés dans les travaux de Tsygan, Keller). La motivation principale vient de la théorie de Hodge non-commutative au sens de Katzarkov--Kontsevich--Pantev. En géométrie algébrique, la
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Suzuki, Takeru. "A theory of lexical functors : light heads in the lexicon and the syntax." Thesis, 1997. http://hdl.handle.net/2429/8609.

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This thesis advances a specific model of 1-syntax, based on Hale and Keyser (1993, 1994) and Dechaine (1996) as a point of departure, and also proposes a general theory of the relation between the lexicon and the syntax. One of the essential proposals that I make is the F\mctionalization Principle, which permits a lexical head to project a functional projection if and only if the meaning of the head is represented by 1-syntactic structure without any extra semantic features. I refer to this type of head as a light head. The Functionalization Principle leads us to a principled account o
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Francis, Elaine Jones. "Variation within lexical categories /." 1999. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9934052.

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Books on the topic "General theory of categories and functors"

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Jiří, Adámek. Automata and algebras in categories. Kluwer Academic Publishers, 1990.

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Colored operads. American Mathematical Society, 2016.

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Bernstein, Joseph. Equivariant sheaves and functors. Springer-Verlag, 1994.

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Ausoni, Christian, 1968- editor of compilation, Hess, Kathryn, 1967- editor of compilation, Johnson Brenda 1963-, Lück, Wolfgang, 1957- editor of compilation, and Scherer, Jérôme, 1969- editor of compilation, eds. An Alpine expedition through algebraic topology: Fourth Arolla Conference, algebraic topology, August 20-25, 2012, Arolla, Switzerland. American Mathematical Society, 2014.

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A notional theory of syntactic categories. Cambridge University Press, 1997.

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A unified theory of syntactic categories. Foris Publications, 1985.

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Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. American Mathematical Society, 2013.

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Fröhlich, Jürg. Quantum groups, quantum categories, and quantum field theory. Springer-Verlag, 1993.

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The study of aspect, tense, and action: Towards a theory of the semantics of grammatical categories. 2nd ed. P. Lang, 1997.

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Bache, Carl. The study of aspect, tense, and action: Towards a theory of the semantics of grammatical categories. P. Lang, 1995.

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Book chapters on the topic "General theory of categories and functors"

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Turaev, Vladimir, and Alexis Virelizier. "Monoidal categories and functors." In Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_1.

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Bakalov, Bojko, and Alexander Kirillov. "3-dimensional topological quantum field theory." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/05.

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Johann, Patricia, and Andrew Polonsky. "Deep Induction: Induction Rules for (Truly) Nested Types." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_18.

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AbstractThis paper introduces deep induction, and shows that it is the notion of induction most appropriate to nested types and other data types defined over, or mutually recursively with, (other) such types. Standard induction rules induct over only the top-level structure of data, leaving any data internal to the top-level structure untouched. By contrast, deep induction rules induct over all of the structured data present. We give a grammar generating a robust class of nested types (and thus ADTs), and develop a fundamental theory of deep induction for them using their recently defined semantics as fixed points of accessible functors on locally presentable categories. We then use our theory to derive deep induction rules for some common ADTs and nested types, and show how these rules specialize to give the standard structural induction rules for these types. We also show how deep induction specializes to solve the long-standing problem of deriving principled and practically useful structural induction rules for bushes and other truly nested types. Overall, deep induction opens the way to making induction principles appropriate to richly structured data types available in programming languages and proof assistants. Agda implementations of our development and examples, including two extended case studies, are available.
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"Categories and Functors." In Saturated Model Theory. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812833822_0026.

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"3. Categories And Functors." In Algebraic Graph Theory. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110617368-003.

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"Derived Categories and Derived Functors." In Etale Cohomology Theory. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814675093_0006.

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"Derived Categories and Derived Functors." In Etale Cohomology Theory. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814307734_0006.

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"Chapter 3. Categories and functors." In Algebraic Graph Theory. DE GRUYTER, 2011. http://dx.doi.org/10.1515/9783110255096.48.

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"Categories, functors and natural transformations." In Category Theory and Applications. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813231078_0002.

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"Categories, functors and natural transformations." In Category Theory and Applications, 2nd ed. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811236099_0002.

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Conference papers on the topic "General theory of categories and functors"

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Howell, Larry L., and Ashok Midha. "A Generalized Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0293.

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Abstract Compliant mechanisms gain at least some of their motion from flexible members. The combination of large-deflection beam analysis, kinematic motion analysis, and energy storage makes the analysis of compliant mechanisms difficult. The design of mechanisms often requires iteration between synthesis and analysis procedures. In general, the difficulty in analysis has limited the use of compliant mechanisms to applications where only simple functions and motions are required. The pseudo-rigid-body model concept promises to be the key to unifying the compliant and rigid-body mechanism theor
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Kitamura, Yoshinobu, Sunao Takafuji, and Riichiro Mizoguchi. "Towards a Reference Ontology for Functional Knowledge Interoperability." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35373.

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Functionality is one of the key aspects of artifact models for design. A function of a device, however, can be captured in different ways in different domains or by different model-authors. Much research on functions has been conducted in the areas of engineering design, functional representation and philosophy, although there are several definitions and notions of functions. We view conceptualization of function is multiplicative in nature: different functions can be captured simultaneously from an objective behavior of an artifact under different teleological contexts of users/designers, or
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Ottosson, Hans, Emma Hirschi, Christopher A. Mattson, and Eric Dahlin. "A Simple Starting Point for Designing for and/or Assessing the Social Impact of Products." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67586.

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In this paper we present a starting point for designing for and/or assessing the social impact of engineered products. The starting point is a set of tables comprising products, their general functional characteristics, and the accompanying social impacts. We have constructed these tables by first extracting a set of social impact categories from the literature, then 65 products were qualitatively reviewed to find their social impact. The resulting product impact tables can be used at either the beginning of the product development process to decide what social impact to design for and discove
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Darbinyan, H. V. "Function and Mechanism Formalization in Task Based Conceptual Design Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-90006.

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Mechanism and function formalization problem is touched in a novel task based conceptual mechanical design method. The general concept and a specific application of this method were reported in earlier publications. Direct dependence between the function and mechanism, identical synthesis tools for various stages of design and for various mechanical objects are the features making the suggested method advantageously different from existing concept design approaches. The core idea of suggested conceptual design method is the direct relation between challenged function and the mechanical entity
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Strong, Philip M. "Influence of Passenger Car Suspension Design on Carbody Roll and on Wheel Unloading on Curves at Unbalance Speeds." In IEEE/ASME/ASCE 2008 Joint Rail Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/jrc2008-63038.

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Analytical results indicate that there is a wide variation in roll and lateral behavior on curves at unbalance speeds, for passenger car suspensions in use today. This paper categorizes passenger car types and analyzes behavior under the action of quasi-static lateral forces such as can occur on curves. Understanding this behavior can be important in providing guidelines for developing new designs that operate at relatively high unbalance speeds while still retaining safe operation, good ride quality and other performance related to suspension system design. The approach taken is to develop eq
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Renze, Wang, Zhang Jiangang, Yang Yapeng, et al. "Emergency Action Level Study in Reprocessing Facility." In 2020 International Conference on Nuclear Engineering collocated with the ASME 2020 Power Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/icone2020-16052.

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Abstract The safety characteristics and potential hazards of reprocessing facilities are different from those of nuclear power plants (NPPs). Emergency action level (EAL) development is an important aspect of emergency preparedness, and EAL is an important basis for emergency response of reprocessing facilities. EAL quantitative research can enhance its operability. At present, the domestic and foreign literature, generally only gave the principle method for EAL development. There are no operational guidance documents for specific EAL quantification in reprocessing facilities. According to the
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Greene, M. Steven, Yu Liu, Wei Chen, Wing Kam Liu, and Hong-Zhong Huang. "Enabling Integrated Material and Product Design Under Uncertainty Through Stochastic Constitutive Relations." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28917.

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This paper presents a computational framework that mathematically propagates material microstructure uncertainties to coarser system resolutions for use in multiscale design frameworks. The computational framework uses a homogenized stochastic constitutive relation that links microstructure uncertainty with stochastic material properties. The stochastic constitutive relation formulated in this work serves as the critical link between the material and product domains in integrated material and product design. Ubiquitous fine resolution uncertainty sources influencing prediction of material prop
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Ye, Xiaoli, and John K. Gershenson. "Attribute Attribute-Based Clustering for Product Family Design." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34885.

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As manufacturers are forced by today’s marketplace to provide nearly customized products to satisfy individual customer requirements and simultaneously achieve economies of scale during production, product family design and platform-based product development have garnered their attention. Determining which elements (attributes, functions, components, etc.) should be made common, variable, or unique, across a product family is the critical step in the successful implementation of product families and product platforms. Therefore, the inherent challenge in product family design is to balance the
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Li, S. Z., J. J. Yu, X. Pei, Hai-jun Su, J. B. Hopkins, and M. L. Culpepper. "Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part III—Numerations and Synthesis of Flexure Mechanisms." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28963.

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In recent years, the increasing of application requirements call for development of a variety of flexure mechanisms with high precision or large motion and both. Therefore, in Part III of this series of papers we demonstrate how to use the methodology addressed in Part I to synthesize concepts for two kinds of flexure mechanisms, i.e. kinematics-type flexure mechanisms (KFMs) and constraint-type flexure mechanisms (CFMs) with the specified-DOF (Degree of Freedom) characteristics. Although most of them utilize parallel configurations and flexure elements, there is a clear difference in the beha
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Ozcan, Arif. "New approaches in smart packaging technologies." In 10th International Symposium on Graphic Engineering and Design. University of Novi Sad, Faculty of technical sciences, Department of graphic engineering and design,, 2020. http://dx.doi.org/10.24867/grid-2020-p1.

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Customer expectations have changed due to the developing technology and changing and improving product variety. This has led the printing industry, the packaging sector in particular, to grow considerably. The food industry along with the increasing need to preserve food long periods of time have led to the need to develop methods that preserve the freshness and safety of food products during their shelf-life. For this reason, attention was paid to packaging systems to facilitate food processing, preserve food quality, extend shelf-life, and prevent the food from spoiling. Thanks to these syst
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