A projective presentation of an object is a realization of that object as a suitable quotient of a projective object.
In homological algebra projective presentations can sometimes be used in place of genuine projective resolutions in the computation of derived functors. See for instance at Ext-functor for examples.
The dual notion is that of injective presentation.
Let be an abelian category. For any object, a projective presentation of is a short exact sequence of the form
hence exhibiting as the cokernel
such that is a projective object.
projective object, projective presentation, projective cover, projective resolution
injective object, injective presentation, injective envelope, injective resolution
flat object, flat resolution
Last revised on September 4, 2012 at 20:29:40. See the history of this page for a list of all contributions to it.