chain homotopy

1. Definition

Let 20240119-chain_homotopy_3038b4682e1f6d64ae501574b4029ad43f8f615e.svg be an abelian category and 20240119-chain_homotopy_e38ff9d36f1c926d54744b7f2a7458227905f13d.svg be the category of chain complexes Suppose 20240119-chain_homotopy_dc9fa149feb22bbd8706da8ac221d425a75ebf1d.svg are chain complexes and 20240119-chain_homotopy_7770b470dffef2dd8dbdab90c59a1068ebf8a59e.svg chain maps

A chain homotopy between 20240119-chain_homotopy_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg and 20240119-chain_homotopy_50706fcb59084c951cf44498a2491f2cd0455273.svg consists of morphisms

20240119-chain_homotopy_994e314e595c1e6eff6aa69a0c150b47933049aa.svg

or (in general not commuting!)

20240119-chain_homotopy_bec40e81eaf80f0418b550186900f300714c74b9.svg

such that

20240119-chain_homotopy_99e969c31d8964f195d5c658b322698891728fb4.svg

or equivalently

20240119-chain_homotopy_2ea75f02359367a688b47cec89fd2310fb0e23c9.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-19 Sa 22:00