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A degree-preserving morphism between chain complexes that commutes with the differentials.
The analogous definition for cochain complexes uses the same commuting-square condition with cohomological grading.
wp-chain-mapnlab-chain-mapstacks-complexesEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the degreewise maps to satisfy the chain-map squares .
Feed several structures into a construction junction and impose compatibility between them.
wp-chain-mapnlab-chain-mapstacks-complexesEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
For a chain map , the mapping cone combines with and uses a differential incorporating both the original differentials and .
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
hatcher-algebraic-topologystacks-derived-categoryThis is an authored directed relation from the source endpoint to the target endpoint.
Require the induced morphism on every homology object to be an isomorphism.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-quasi-isomorphismnlab-quasi-isomorphismstacks-quasi-isomorphism