## Handbook of Categorical Algebra: Volume 2, Categories and StructuresThe Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users. |

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### Contents

Regular categories | 89 |

Algebraic theories | 122 |

Monads | 186 |

Accessible categories | 254 |

Enriched category theory | 291 |

Topological categories | 349 |

Fibred categories | 373 |

Bibliography | 436 |

### Other editions - View all

Handbook of Categorical Algebra: Volume 2, Categories and Structures Francis Borceux No preview available - 2008 |

### Common terms and phrases

a-filtered abelian category additive adjunction algebraic theory already Applying arrow axiom bijections canonical cartesian choose coequalizer Coker colim colimit commutative compact complete composite conclude cone consider construction continuous Conversely corresponding define definition diagram elements equalizer equivalence relation equivalent exact sequence example exists fact factorization faithful fibration fibre filtered Finally finite finite limits functor F given giving holds identity immediately implies isomorphism kernel pair left adjoint lemma limits locally mapping means models Modt monad monomorphism Moreover morphism natural transformation notation notion object observe obvious operation particular phism precisely presentable preserves Proof Proposition prove pullback reflects regular cardinal regular epimorphism relation ring satisfies small category spaces structure subcategory subset suffices suppose symmetric monoidal closed T-algebras theorem topology unique unit universal volume write yields zero