Cocycle category

In category theory, a branch of mathematics, the cocycle category of objects "X", "Y" in a model category is a category in which the objects are pairs of maps formula_1 and the morphisms are obvious commutative diagrams between them. It is denoted by formula_2. (It may also be defined using the language of 2-category.)
One has: if the model category is right proper and is such that weak equivalences are closed under finite products,
is bijective.