Results 21 to 30 of about 791 (171)
Natural Transformations as Rewrite Rules and Monad Composition [PDF]
Logical Methods in Computer Science, 2019 Eklund et al. (2002) present a graphical technique aimed at simplifying the verification of various category-theoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting.
Dexter Kozen
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Quotient-Comprehension Chains [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic, but also in ...
Kenta Cho +3 more
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A Linear/Producer/Consumer Model of Classical Linear Logic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?.
Jennifer Paykin, Steve Zdancewic
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An axiomatic approach to forcing and generic extensions
Comptes Rendus. Mathématique, 2020 This paper provides a conceptual analysis of forcing and generic extensions. Our goal is to give general axioms for the concept of standard forcing-generic extension and to show that the usual (poset) constructions are unified and explained as ...
Freire, Rodrigo A.
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On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group
Journal of Mathematics, 2021 The paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold associated with a time parameter.
M. Abu-Saleem, Omar Almallah
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The Expectation Monad in Quantum Foundations [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the distribution and ultrafilter monad, and on the other hand the continuation ...
Bart Jacobs, Jorik Mandemaker
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Relational Algebra by Way of Adjunctions [PDF]
, 2018 Bulk types such as sets, bags, and lists are monads, and therefore support a notation for database queries based on comprehensions. This fact is the basis of much work on database query languages.
Wu, N +7 more
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Logical Methods in Computer Science, 2014 We investigate the phenomenon that "every monad is a linear state monad". We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value calculus.
Rasmus Ejlers Møgelberg, Sam Staton
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General affine adjunctions, Nullstellensätze, and dualities [PDF]
, 2014 We develop an abstract categorical framework that generalises the classical "system-solution" adjunction in algebraic geometry, proving that such adjunctions take place in a multitude of contexts.
Caramello, O., Spada, L., Marra, V.
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Homotopy theory of modules over diagrams of rings
Proceedings of the American Mathematical Society, Series B, 2014 Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories ℳ(𝓈) (as 𝓈 runs through the diagram ...
J. P. C. Greenlees, B. Shipley
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