Results 21 to 30 of about 399,672 (159)
, 2018 Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations.
Marquis, Jean-Pierre
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Modalities in homotopy type theory
, 2020 Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes.
Rijke, Egbert +2 more
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Category theory and set theory as theories about complementary types of universals [PDF]
, 2016 Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals.
Ellerman, David P.
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The Conformal Characters [PDF]
, 2018 We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules.
Bourget, Antoine, Troost, Jan
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On Self-Predicative Universals in Category Theory
, 2015 1. This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and ...
Ellerman, David
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Object-Free Definition of Categories [PDF]
, 2013 Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach ...
Riccardi, Marco
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A non-standard analysis of a cultural icon: The case of Paul Halmos
, 2016 We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism.
Blaszczyk, Piotr +6 more
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Categories without structures [PDF]
, 2009 The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics.
Rodin, Andrei
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Category theory : definitions and examples [PDF]
, 1990 Category theory was invented as an abstract language for describing certain structures and constructions which repeatedly occur in many branches of mathematics, such as topology, algebra, and logic.
Srinivas, Yellamraju V.
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Semantics of higher inductive types
, 2019 Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style.
Lumsdaine, Peter LeFanu, Shulman, Mike
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