Results 11 to 20 of about 791 (171)
Where Do Adjunctions Come From? Chimera Morphisms and Adjoint Functors in Category Theory [PDF]
FoundationsCategory theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints come from”. The
David Ellerman
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, 1994 We present the category-theoretic notion of adjunction in a way that makes it easy to formally <i>calculate</i> with it; an acquaintance with its algebraic properties may greatly help in understanding the notion. It is illustrated by means of a lot of theorems and proofs.
Fokkinga, M.M., Meertens, Lambert
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General affine adjunctions, Nullstellensätze, and dualities [PDF]
, 2021 We introduce and investigate a category-theoretic abstraction of the standard "system-solution" adjunction in affine algebraic geometry. We then look further into these geometric adjunctions at different levels of generality, from syntactic categories to
Olivia Caramello +3 more
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Arboreal Categories: An Axiomatic Theory of Resources [PDF]
Logical Methods in Computer Science, 2023 Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures.
Samson Abramsky, Luca Reggio
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Logic Journal of the IGPL, 2023 Abstract Let $\varSigma $ be a signature without $0$-ary operation symbols and $\textsf{Sl}$ the category of semilattices. Then, after defining and investigating the categories $\int ^{\textsf{Sl}}\textrm{Isys}_{\varSigma }$, of inductive systems of $\varSigma $-algebras over all semilattices, which are ordered pairs $\boldsymbol ...
Climent Vidal, J. +1 more
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Categorical Equivalences from State-Effect Adjunctions [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 From every pair of adjoint functors it is possible to produce a (possibly trivial) equivalence of categories by restricting to the subcategories where the unit and counit are isomorphisms.
Robert Furber
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Hopf and Lie algebras in semi-additive Varieties [PDF]
Logical Methods in Computer Science, 2017 We study Hopf monoids in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor.
Hans-E. Porst
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Relating Idioms, Arrows and Monads from Monoidal Adjunctions [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 We revisit once again the connection between three notions of computation: monads, arrows and idioms (also called applicative functors). We employ monoidal categories of finitary functors and profunctors on finite sets as models of these notions of ...
Exequiel Rivas
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Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and ...
Yoshihiro Maruyama
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Monads need not be endofunctors [PDF]
Logical Methods in Computer Science, 2015 We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed containers.
Thosten Altenkirch +2 more
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