on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
For $\mathcal{C} \underoverset{\underset{R}{\longrightarrow}}{\overset{L}{\longleftarrow}}{{}_{\phantom{Qu}}\bot_{Qu}}\mathcal{D}$ a Quillen adjunction between model categories, also the corresponding left and right derived functors form a pair of adjoint functors
between the corresponding homotopy categories.
Moreover, the adjunction unit and adjunction counit of this derived adjunction are the images of the derived adjunction unit and derived adjunction counit of the original Quillen adjunction.
For full proof see also at Introduction to Homotopy Theory this Prop., or at geometry of physics – categories and toposes this Prop..
Last revised on July 12, 2021 at 08:58:30. See the history of this page for a list of all contributions to it.