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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeApr 14th 2020

    Recorded definition and basic properties.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 4th 2023



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

    The wreath product of Δ\Delta and an EZ-category (also known as the Θ\Theta-construction) is again an EZ-category (Bergner–Rezk, Proposition 4.3). In particular, Joyal’s category Θ n\Theta_n is an EZ-category for all n0n\ge0.

    Segal’s category Γ\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 Λ\Lambda and the category of trees Ω\Omega are EZ-categories (Berger–Moerdijk, Examples 6.8).

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

    The category of cubes QQ (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