2022-03-25-quick_note

1— date: 2022-03-25 tags: [quick_notes] —

2022-03-25

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19:05

An interesting observation:

For /\((A, {\partial})\in \mathsf{Ch}{\mathsf{R}{\hbox{-}}\mathsf{Mod}}\) a chain complex, \(H^*(A) = {\ker {\partial}\over \operatorname{im}{\partial}}\) and \(Z(A) = \mathop{\mathrm{Hom}}_{\mathsf{Ch}{\mathsf{R}{\hbox{-}}\mathsf{Mod}}}(k[0]. A)\) and \(B(A) = Z(A)/\sim\) where one mods out by nullhomotopic morphism?

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