Quillen Adjunction

In homotopy theory, a branch of mathematics, a Quillen adjunction between two closed model categories C and D is a special kind of adjunction between categories that induces an adjunction between the homotopy categories Ho(C) and Ho(D) via the total derived functor construction. Quillen adjunctions are named in honor of the mathematician Daniel Quillen.

Read more about Quillen AdjunctionFormal Definition, Properties

Other articles related to "quillen adjunction, quillen, adjunction":

Quillen Adjunction - Properties
... It is a consequence of the axioms that a left (right) Quillen functor preserves weak equivalences between cofibrant (fibrant) objects ... The total derived functor theorem of Quillen says that the total left derived functor LF Ho(C) → Ho(D) is a left adjoint to the total right derived functor RG Ho(D) → Ho(C) ... This adjunction (LF, RG) is called the derived adjunction ...