The Stacks project

  • If $\varphi _*$ and $\psi _*$ are homotopic, and $A_* \to B_*$ is a homomorphism of cosimplicial rings, then

    \[ \varphi _* \otimes 1, \psi _* \otimes 1 : K_* \otimes _{A_*} B_* \longrightarrow M_* \otimes _{A_*} B_* \]

    are homotopic as homomorphisms of cosimplicial $B_*$-modules.

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