## Handbook of Categorical Algebra 2: Categories and Structures, Volume 2 |

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### Contents

Regular categories | 89 |

Algebraic theories | 122 |

Monads | 186 |

Copyright | |

5 other sections not shown

### Common terms and phrases

a-filtered abelian category additive adjunction algebraic theory already Applying arrow axiom bijections canonical cartesian choose closed category 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 Finally finite finite limits functor F given giving holds identity immediately implies isomorphism kernel pair left adjoint lemma locally mapping means models monad monomorphism morphism natural transformation notation notion object observe obvious operation particular phism presentable preserves Proof Proposition prove pullback reflects regular cardinal regular epimorphism relation remains ring satisfies small category spaces structure subset suffices T-algebras theorem theory topological unique unit universal volume write yields zero