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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeApr 14th 2020
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexRecorded definition and basic properties. <a href="https://ncatlab.org/nlab/revision/Eilenberg-Zilber+category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Zilber+category">current</a>

   Recorded definition and basic properties.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 4th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: ## Examples The [[category of simplices]] $\Delta$ is an Eilenberg–Zilber category. The [[wreath product]] of $\Delta$ and an EZ-category (also known as the $\Theta$-construction) is again an EZ-category (Bergner–Rezk, Proposition 4.3). In particular, Joyal's category $\Theta_n$ is an EZ-category for all $n\ge0$. Segal's category $\Gamma$ (used to define [[Gamma-spaces]]) is an EZ-category (Berger–Moerdijk, Examples 6.8). The category of [[symmetric simplices]] (inhabited finite sets and their maps) is an EZ-category (Berger–Moerdijk, Examples 6.8). The [[cyclic category]] $\Lambda$ and the [[category of trees]] $\Omega$ are EZ-categories (Berger–Moerdijk, Examples 6.8). More generally, the total category $\mathbf{R}G$ of a crossed group $G$ on an EZ-category $\mathbf{R}$ whose underlying Reedy category is strict is itself an EZ-category (Berger–Moerdijk, Examples 6.8). The [[category of cubes]] $Q$ (generated by faces and degeneracies, without connections, symmetries, reversals, or diagonals) is an EZ-category (Isaacson, Proposition 4.4). The category of symmetric cubes with min-connections (Isaacson, Definition 3.4, Proposition 3.11) is an EZ-category (Isaacson, Proposition 4.4). <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Zilber+category/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Zilber+category/5">v5</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Zilber+category">current</a>

   Added:

   Examples

   The category of simplices $\Delta$ is an Eilenberg–Zilber category.

   The wreath product of $\Delta$ and an EZ-category (also known as the $\Theta$-construction) is again an EZ-category (Bergner–Rezk, Proposition 4.3). In particular, Joyal’s category $\Theta_n$ is an EZ-category for all $n\ge0$.

   Segal’s category $\Gamma$ (used to define Gamma-spaces) is an EZ-category (Berger–Moerdijk, Examples 6.8).

   The category of symmetric simplices (inhabited finite sets and their maps) is an EZ-category (Berger–Moerdijk, Examples 6.8).

   The cyclic category $\Lambda$ and the category of trees $\Omega$ are EZ-categories (Berger–Moerdijk, Examples 6.8).

   More generally, the total category $\mathbf{R}G$ of a crossed group $G$ on an EZ-category $\mathbf{R}$ whose underlying Reedy category is strict is itself an EZ-category (Berger–Moerdijk, Examples 6.8).

   The category of cubes $Q$ (generated by faces and degeneracies, without connections, symmetries, reversals, or diagonals) is an EZ-category (Isaacson, Proposition 4.4).

   The category of symmetric cubes with min-connections (Isaacson, Definition 3.4, Proposition 3.11) is an EZ-category (Isaacson, Proposition 4.4).

   diff, v5, current

3. • CommentRowNumber3.
   • CommentAuthorncfavier
   • CommentTimeSep 29th 2024
   • PermaLink
   Author: ncfavier
   Format: MarkdownItexAdded the cartesian cube category. <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Zilber+category/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Zilber+category/7">v7</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Zilber+category">current</a>

   Added the cartesian cube category.

   diff, v7, current