homology functor

1. Definition / Proposition

Let 20230817-homology_functor_81ca28a09975fbedac4572d53c0b7c3d6395ae46.svg be the category of chain complexes for an abelian category 20230817-homology_functor_eb04be82533afa6bcab2b0d2106fd2828974c0d1.svg, then the homology functor is defined as

20230817-homology_functor_b83bb27ee11ec3d37d185fa222533d85f3d6661a.svg

where

  1. 20230817-homology_functor_3099d5a42c4b3f46c692eeeb685db8033d0c724b.svg is given as colimit
20230817-homology_functor_85920b7fe047ba41f84dab64515bac34f860127e.svg
  1. the morphism is given as morphism induced by
20230817-homology_functor_37f6238d2ba83056d73cb2d6942d9c15bc9074ca.svg

see:

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 15:55