Reedy category
Type of category in mathematics
From Wikipedia, the free encyclopedia
In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure. A prototypical example is the simplex category or its opposite. It was introduced by Christopher Reedy in his unpublished manuscript.[1]
Definition
A Reedy category consists of the following data: a category R, two wide (lluf) subcategories and a functorial factorization of each map into a map in followed by a map in that are subject to the condition: for some total preordering (degree), the nonidentity maps in lower or raise degrees.[2]
Note some authors such as nlab require each factorization to be unique.[3][4]
Reedy model structure
A Reedy model structure is a canonical model-category structure placed on the functor category M^R when R is a Reedy category and M is a model category.
Eilenberg–Zilber category
An Eilenberg–Zilber category is a variant of a Reedy category.
