Categories and Computability
نویسنده
چکیده
2 Categories and examples 7 2.1 The definition of a category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Categories as graphs with composition . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Categories as partial semigroups . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Categories as enriched categories . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 The opposite category and duality . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Examples of categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Preorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 Finite categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.3 Categories enriched in finite sets . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.4 Monoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.5 Path categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.6 Matrices over a rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.7 Kleene categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.8 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.9 Programming languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.10 Products and sums of categories . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.11 Slice categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
منابع مشابه
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