Homology |
Contents
Modules Diagrams and Functors 1 The Arrow Notation | 1 |
Modules | 2 |
Diagrams | 3 |
Copyright | |
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A₁ abelian category additive relation automorphism B₁ bar resolution bifunctor bimodule boundary chain complex chain transformation coefficients cohomology composite congruence connecting homomorphisms construct contracting homotopy contravariant corresponding couniversal covariant functor cycle defined definition degree denote DG-algebra differential dimension dual E₁ element epic epimorphism equivalent extension factor set filtration finite formula free abelian group free module function given gives graded algebra graded modules hence homo homology groups homomorphism f identity II-module implies induced injective integers inverse K-algebra kernel left R-module Lemma long exact sequence module homomorphism monic monomorphism morphism natural isomorphism object pair phism projective resolution Proof Prop Proposition prove quotient R-module right R-module ring short exact sequence simplicial singular spectral sequence splits subgroup submodule tensor product torsion product transformation f unique vector space yields Z(II zero