Relevant bibliographies by topics / Bicomplete categories

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Bicomplete categories'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Bicomplete categories"

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Santocanale, Luigi. "μ-Bicomplete Categories and Parity Games". RAIRO - Theoretical Informatics and Applications 36, № 2 (2002): 195–227. http://dx.doi.org/10.1051/ita:2002010.

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Tang, Guoliang. "Abelian model structures on comma categories." Ukrains’kyi Matematychnyi Zhurnal 76, no. 3 (2024): 373–81. http://dx.doi.org/10.3842/umzh.v76i3.7289.

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UDC 512.64 Let A and B be bicomplete Abelian categories, which both have enough projectives and injectives and let T : A → B be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on A and B can be amalgamated into a global hereditary Abelian model structure on the comma category ( T ↓ B ) . As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.
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Chen, Wenjing, Zhongkui Liu, and Xiaoyan Yang. "Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs." Journal of Algebra and Its Applications 17, no. 09 (2018): 1850180. http://dx.doi.org/10.1142/s0219498818501803.

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In this paper, we investigate the homotopy categories [Formula: see text] and [Formula: see text] with respect to a complete and hereditary cotorsion pair [Formula: see text] in a bicomplete abelian category. We prove that [Formula: see text] is compactly generated provided that [Formula: see text] is compactly generated. We introduce and characterize Gorenstein [Formula: see text]-complexes with respect to [Formula: see text] and show that a complex is a Gorenstein [Formula: see text]-complex if and only if its every term is a Gorenstein [Formula: see text]-object. We also show that the inclu
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4

Ion, C. Baianu, Georgescu George, F. Glazebrook James, and Brown Ronald. "BRAIN Journal - Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 1–11. https://doi.org/10.5281/zenodo.1037321.

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ABSTRACT The fundamentals of ÃLukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the Schr¨odinger representation, with both initial and boundary
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Cirici, Joana, Daniela Egas Santander, Muriel Livernet, and Sarah Whitehouse. "Model category structures and spectral sequences." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (2019): 2815–48. http://dx.doi.org/10.1017/prm.2019.45.

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AbstractLet R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.
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Santocanale, Luigi. "A Calculus of Circular Proofs and its Categorical Semantics." BRICS Report Series 8, no. 15 (2001). http://dx.doi.org/10.7146/brics.v8i15.20472.

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<p>We present a calculus of proofs, the intended models of which<br />are categories with finite products and coproducts, initial algebras<br />and final coalgebras of functors that are recursively constructible<br />out of these operations, that is, mu-bicomplete categories. The <br />calculus satisfies the cut elimination and its main characteristic is<br />that the underlying graph of a proof is allowed to contain a <br />certain amount of cycles. To each proof of the calculus we associate<br />a system of equations which has a meaning in ever
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Savage, Rhiannon. "Koszul Monoids in Quasi-abelian Categories." Applied Categorical Structures 31, no. 6 (2023). http://dx.doi.org/10.1007/s10485-023-09756-7.

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AbstractSuppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $$\mathcal {E}$$ E with enough flat projectives, such as the category of complete bornological spaces $${{\textbf {CBorn}}}_k$$ CBorn k or the category of inductive limits of Banach spaces $${{\textbf {IndBan}}}_k$$ IndBan k . Working with monoids in $$\mathcal {E}$$ E , we can generalise and extend the Koszul duality theory of Beilinson, Ginzburg, Soergel. We use an element-free approach to define the notions of Koszul monoids, and quadratic monoids and their duals. Schneiders’ embedding of a quasi-abel
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8

Calmès, Baptiste, Emanuele Dotto, Yonatan Harpaz, et al. "Hermitian K-theory for stable $$\infty $$-categories I: Foundations." Selecta Mathematica 29, no. 1 (2022). http://dx.doi.org/10.1007/s00029-022-00758-2.

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AbstractThis paper is the first in a series in which we offer a new framework for hermitian $${\text {K}}$$ K -theory in the realm of stable $$\infty $$ ∞ -categories. Our perspective yields solutions to a variety of classical problems involving Grothendieck-Witt groups of rings and clarifies the behaviour of these invariants when 2 is not invertible. In the present article we lay the foundations of our approach by considering Lurie’s notion of a Poincaré $$\infty $$ ∞ -category, which permits an abstract counterpart of unimodular forms called Poincaré objects. We analyse the special cases of
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Dissertations / Theses on the topic "Bicomplete categories"

1

Fortier, Jerome. "Puissance expressive des preuves circulaires." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4779/document.

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Cette recherche vise à établir les propriétés fondamentales d'un système formel aux preuves circulaires introduit par Santocanale, auquel on a rajouté la règle de coupure. On démontre, dans un premier temps, qu'il y a une pleine correspondance entre les preuves circulaires et les flèches issues des catégories dites µ-bicomplètes. Ces flèches sont celles que l'on peut définir purement à partir des outils suivants: les produits et coproduits finis, les algèbres initiales et les coalgèbres finales. Dans la catégorie des ensembles, les preuves circulaires dénotent donc les fonctions qu'on peut déf
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Book chapters on the topic "Bicomplete categories"

1

May, J., and J. Sigurdsson. "Topologically bicomplete model categories." In Parametrized Homotopy Theory. American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/132/04.

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