Formal Definition
Given two closed model categories C and D, a Quillen adjunction is a pair
- (F, G): C D
of adjoint functors with F left adjoint to G such that F preserves cofibrations and trivial cofibrations or, equivalently by the closed model axioms, such that G preserves fibrations and trivial fibrations. In such an adjunction F is called the left Quillen functor and G is called the right Quillen functor.
Read more about this topic: Quillen Adjunction
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)