Results 21 to 30 of about 789 (269)
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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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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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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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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