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A graded object with degree differential squaring to zero.
The zero composite requires zero morphisms; preadditive categories suffice. Homology objects require additional kernel/image or abelian hypotheses.
wp-chain-complexnlab-chain-complexstacks-complexesstacks-abelian-categoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Add boundary maps with .
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
stacks-complexeswp-chain-complexnlab-chain-complexstacks-derived-textEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply two chain complexes in one additive category together with degreewise maps between them.
Feed several structures into a construction junction and impose compatibility between them.
wp-chain-mapnlab-chain-mapstacks-complexesThis is an authored directed relation from the source endpoint to the target endpoint.
The singular chain complex of a topological space is a particular chain complex, freely generated by singular simplices with the alternating-face boundary.
The target is a member or subtype of the broader source class.
hatcher-algebraic-topology