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Relevant bibliographies by topics / Functorial preservation

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Journal articles

Academic literature on the topic 'Functorial preservation'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Functorial preservation"

1

Knauer, Ulrich, Yanming Wang, and Xia Zhang. "Functorial properties of Cayley consructions." Acta et Commentationes Universitatis Tartuensis de Mathematica 10 (December 31, 2006): 17–29. http://dx.doi.org/10.12697/acutm.2006.10.02.

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We describe the construction of the Cayley graph of a semigroup as a functor and investigate certain reflection and preservation properties of this functor. We also investigate it with respect to several product constructions including pullbacks.

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2

Gao, Nan, Julian Külshammer, Sondre Kvamme, and Chrysostomos Psaroudakis. "A functorial approach to monomorphism categories for species I." Communications in Contemporary Mathematics, October 5, 2021. http://dx.doi.org/10.1142/s0219199721500693.

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We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalized species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit c

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3

Gao, Nan, Julian Külshammer, Sondre Kvamme, and Chrysostomos Psaroudakis. "A functorial approach to monomorphism categories for species I." Communications in Contemporary Mathematics, October 5, 2021. http://dx.doi.org/10.1142/s0219199721500693.

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Abstract:

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalized species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit c

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4

BOTTA, NICOLA, NURIA BREDE, PATRIK JANSSON, and TIM RICHTER. "Extensional equality preservation and verified generic programming." Journal of Functional Programming 31 (2021). http://dx.doi.org/10.1017/s0956796821000204.

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Abstract In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $$f,g \, : \, A \, \to \, B$$ are extensionally equal, that is, $$\forall x \in A$$ , $$f \, x = g \, x$$ , then $$map \, f \, : \, List \, A \to

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5

Fürer, Basil, Andreas Lochbihler, Joshua Schneider, and Dmitriy Traytel. "Quotients of Bounded Natural Functors." Logical Methods in Computer Science Volume 18, Issue 1 (February 1, 2022). http://dx.doi.org/10.46298/lmcs-18(1:23)2022.

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The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve the BNF structure. In this article, we tackle the preservation question for quotients, the last important principle for introducing new types in HOL. We identify sufficient conditions under which a quotient inherits the BNF str

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6

Mesland, Bram, and Mehmet Haluk Şengün. "Equal rank local theta correspondence as a strong Morita equivalence." Selecta Mathematica 30, no. 4 (2024). http://dx.doi.org/10.1007/s00029-024-00966-y.

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AbstractLet (G, H) be one of the equal rank reductive dual pairs $$\left( Mp_{2n},O_{2n+1} \right) $$ M p 2 n , O 2 n + 1 or $$\left( U_n,U_n \right) $$ U n , U n over a nonarchimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain subsets, say $$\widehat{G}_\theta $$ G ^ θ and $$\widehat{H}_\theta $$ H ^ θ , of the tempered duals of G and H. We prove that this bijection arises from an equivalence between the categories of representations of two $$C^*$$ C ∗ -algebras whose spectra are $$\widehat{G}_\theta $$ G ^ θ and

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7

Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o

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