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Axiomatizing a category of categories

Journal of Symbolic Logic, 1991
AbstractElementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed
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The Kleisli Category is a Category Of Fractions

Quaestiones Mathematicae, 2002
Abstract unavailable at this time..> Mathematics Subject Classification (2000): 18C20, 18A99 Quaestiones Mathematicae 25 (2002), 397 ...
J.J.C. Vermeulen   +2 more
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Categories of Categories and Categories of Functors

1972
The composition of functors in 2.2.6 suggests the study of categories whose objects are categories and whose morphisms are functors. 2.2.7 leads to categories whose objects are functors C→D and whose morphisms are natural transformation. However, familiar antinomies like “the set of all sets.” or “the set of all sets not containing themselves as an ...
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ABSTRACTIONIST CATEGORIES OF CATEGORIES

The Review of Symbolic Logic, 2015
AbstractIf${\cal C}$is a category whose objects are themselves categories, and${\cal C}$has a rich enough structure, it is known that we can recover the internal structure of thecategoriesin${\cal C}$entirely in terms of thearrowsin${\cal C}$. In this sense, the internal structure of the categories in a rich enough category of categories is visible in ...
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