Cocycle category
Category-theoretic construction
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 and the morphisms are obvious commutative diagrams between them.[1] It is denoted by . (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.
References
- ^ Jardine, J. F. (2009). "Cocycle Categories". Algebraic Topology Abel Symposia Volume 4. Berlin Heidelberg: Springer. pp. 185–218. doi:10.1007/978-3-642-01200-6_8. ISBN 978-3-642-01200-6.
- Jardine, J.F. (2007). "Simplicial presheaves" (PDF). Archived from the original (PDF) on 2013-10-17. Retrieved 2013-10-16.