Results 41 to 50 of about 111,083 (181)
Variation on a comprehensive theme [PDF]
arXiv, 2021 The main result concerns a bicategorical factorization system on the bicategory $\mathrm{Cat}$ of categories and functors. Each functor $A\xra{f} B$ factors up to isomorphism as $A\xra{j}E\xra{p}B$ where $j$ is what we call an ultimate functor and $p$ is what we call a groupoid fibration. Every right adjoint functor is ultimate. Functors whose ultimate
arxiv
The Heteromorphic Approach to Adjunctions: Theory and History
MathematicsMallios and Zafiris emphasize that adjoint functors, or adjunctions, are not only “ubiquitous” in category theory but also characterize the naturality of their approach to physical geometry.
David Ellerman
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International Journal of Mathematics and Mathematical Sciences, 2002 We develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-induction functor.
J. Gómez-Torrecillas
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Adjoint functor theorems for lax-idempotent pseudomonads [PDF]
Theory and Applications of Categories, Vol. 41, 2024, No. 20, pp
667-685, 2023 For each pair of lax-idempotent pseudomonads $R$ and $I$, for which $I$ is locally fully faithful and $R$ distributes over $I$, we establish an adjoint functor theorem, relating $R$-cocontinuity to adjointness relative to $I$. This provides a new perspective on the nature of adjoint functor theorems, which may be seen as methods to decompose ...
arxiv
Categories with Foundation [PDF]
, 2020 We develop the theory of categories from foundations up. The thesis culminates in a theorem in which we assert that any concrete functor between categories of models of algebraic theories, where the codomain categories' alphabet does not contain ...
Forsman, David
core
Reflexivity in Derived Categories
, 2009 An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories.
Mantese, Francesca, Tonolo, Alberto
core +1 more source
Transpension: The Right Adjoint to the Pi-type [PDF]
Logical Methods in Computer SciencePresheaf models of dependent type theory have been successfully applied to model HoTT, parametricity, and directed, guarded and nominal type theory. There has been considerable interest in internalizing aspects of these presheaf models, either to make ...
Andreas Nuyts, Dominique Devriese
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The homunculus brain and categorical logic
Zagadnienia Filozoficzne w Nauce, 2020 The interaction between syntax (formal language) and its semantics (meanings of language) is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to create meanings ...
Steve Awodey, Michał Heller
doaj
Induction and restriction as adjoint functors on representations of locally compact groups
International Journal of Mathematics and Mathematical Sciences, 1993 In this paper the Frobenius Reciprocity Theorem for locally compact groups is looked at from a category theoretic point of view.
Robert A. Bekes, Peter J. Hilton
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A note on a free group. The decomposition of a free group functor through the category of heaps [PDF]
arXiv, 2021 This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it to describe a slightly different construction of free groups.
arxiv