Reedy category

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 It was introduced by Christopher Reedy in his unpublished manuscript.^[1]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 ${\displaystyle R_{-},R_{+}}$ and a functorial factorization of each map into a map in ${\displaystyle R_{-}}$ followed by a map in ${\displaystyle R_{+}}$ that are subject to the condition: for some total preordering (degree), the nonidentity maps in ${\displaystyle R_{-},R_{+}}$ lower or raise degrees.^[2]

Note some authors such as nlab require each factorization to be unique.^[3][4]

Reedy model structure

Eilenberg–Zilber category

An Eilenberg–Zilber category is a variant of a Reedy category.