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I have the following basic question on Čech–Alexander complexes. Let $R$ be a ring and $A$ be an $R$-algebra. To this datum one can attach a cosimplicial ring which assigns to an object $[n]=\{0,1,\...

It's well known that Dold-Kan correspondence is an isomorphism between simplicial vector spaces and non-negative chain complexes of vector spaces. Moreover, weak equivalences and fibrations are ...