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Some of the next articles are maybe not open access.
, 2014
Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
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Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
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Lawvere's basic theory of the category of categories
Journal of Symbolic Logic, 1975It is long known that Lawvere's theory in The category of categories as foundations of mathematics A[1] does not work, as indicated in Ishell's review [0]. Isbell there gives a counterexample that CDT—Category Description Theorem—[1, p. 15] is in fact not a theorem of BT (the Basic Theory of [1]) and suggests adding CDT to the axioms.Our starting point
Anne Preller, Georges Blanc
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2011
Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning.
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Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning.
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Category Theory is a Contentful Theory
Philosophia Mathematica, 2014In (Linnebo & Pettigrew, 2011), some objections to category theory as an autonomous foundation are presented. The authors of that paper do a commendable job making clear several distinct senses of “autonomous” as it occurs in the phrase “autonomous foundation.” Unfortunately, the paper seems to treat the “categorist” perspective rather unfairly ...
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Category Theory as an Autonomous Foundation
Philosophia Mathematica, 2011Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy : logical, conceptual, and justificatory. We argue that, while a strong case can be made for its logical and conceptual autonomy, its justificatory autonomy turns on ...
Linnebo, Oystein, Pettigrew, RG
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Category Theory and Foundations
2018In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy.
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, 1977