2022-03-25-quick_note

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

2022-03-25

Refs: ?

19:05

An interesting observation:

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

#untagged