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- W22283 abstract "A chain complex is a sequence of abelian groups and homomorphisms $$ {C_.}:...{text{ }}{C_n}{text{ }}{text{ }}{C_{n - 1}}{text{ }}{text{ }}...$$with the property d n ∘ d n+1 = 0 for all n. Homomorphisms d n are called boundary operators or differentials. A cochain complex is a sequence of abelian groups and homomorphisms $${C^.}:...{text{ }}{C^n}{text{ }}{text{ }}{C_{n + 1}}{text{ }}{text{ }}...$$with the property d n ∘ d n−1 = 0. A chain complex can be considered as a cochain complex by reversing the enumeration: C n = C −n , d n = d −n . This is why we will usually consider only cochain complexes. A complex of A- modules is a complex for which C n (respectively C n ) are modules over a ring A and d n (resp. d n ) are homomorphisms of modules." @default.
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- W22283 date "1994-01-01" @default.
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- W22283 title "The Language of Categories" @default.
- W22283 doi "https://doi.org/10.1007/978-3-642-57911-0_2" @default.
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