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

  1. 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.
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