## What is Category Theory? |

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### Contents

Preface | 7 |

Introducing Categories to the Practicing Physicist | 45 |

Some Implications of the Adoption of Category Theory for Philosophy | 75 |

Sets Categories and Structuralism | 95 |

A Theory of Adjoint Functors with some Thoughts about their | 127 |

Enriched Stratified Systems for the Foundations of Category Theory | 185 |

Category Theory Pragmatism and Operations Universal in Mathematics | 205 |

What is Category Theory? | 221 |

an abstract setting for analogy and comparison | 257 |

On Doing Category Theory within Set Theoretic Foundations | 275 |

### Common terms and phrases

2-category 2-morphisms abstract sets adjoint functors adjunctive square algebraic geometry algebraic topology anti-diagonal map applied arrows axioms basic bifunctor Cartesian category of sets Category Theory chimera chimera morphisms codomain comma category commutative composition concepts concrete construction context corresponding counit deﬁned deﬁnition determination diagram category diﬀerent domain Eilenberg and Mac elements equivalence example existence factorization ﬁeld ﬁnd ﬁnite ﬁrst function functor categories G.Sica Ga,a give given Grothendieck groupoid het-bifunctor Het(x Het(x,a heteromorphisms homology homology theory homomorphism identity invariant Jackendoff knot language Lawvere left adjoint LimD logic Mac Lane Math mathematicians morphisms natural isomorphism natural transformations NFUP notion operations over-and-back pair paper philosophical proof properties quandle quantum reﬂection relation representation right adjoint role self-determination semantics set theory Sica speciﬁc structure subcategory subset surface tensor theoretical topological spaces topos topos theory toposes underlying set unique universal variable x,Fx