## Abelian categories: an introduction to the theory of functors |

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### Contents

Introduction | 1 |

FUNDAMENTALS | 14 |

FUNDAMENTALS OF ABELIAN | 35 |

Copyright | |

6 other sections not shown

### Common terms and phrases

abelian category abelian groups absolutely pure additive functor adjoint functor adjoint functor theorem automorphism class group Axiom category of abelian category of modules category of sets co-well-powered cokernel commutative diagram composition contravariant functor covariant functor defined difference kernel direct sum system dual Dually element embedding theorem epimorphism essential extension exact embedding exact functor exact iff exact sequences exact subcategory Exercise exists family of subobjects finite full subcategory function functor F Given Grothendieck category Hence homomorphism ideal identity map inclusion functor injective cogenerator injective envelope isomorphic lattice left-adjoint left-complete category lemma metatheorem mono functor monomorphism morphism natural transformation naturally equivalent nonzero obtain one-to-one ordinal number pair of maps partially ordered Proof Proposition prove pullback diagram pushout quotient objects right roots right-complete right-exact ring small abelian category small category small projective subobject theory torsion trivial unique map vector spaces well-powered zero object