On an extension of the notion of Reedy category

By C. Berger, Ieke Moerdijk. 2008

132 citations recorded by the source corpus.

We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occurring in topology such as Segal’s category Γ, or the total category of a crossed simplicial group such as Connes’ cyclic category Λ. For any generalized Reedy category $${\mathbb {R}}$$ and any cofibrantly generated model category $${{\mathcal{E}}}$$, the functor category $${{\mathcal{E}}^\mathbb {R}}$$ is shown to carry a canonical model structure of Reedy type.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45857039f56ca22226a3c6d13df72745ec43d8fa

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In Algebra and Number Theory

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Citations in the corpus

Categorical Homotopy Theory (2014, methodology): “preserved by categorical equivalence and includes several new examples of interest to homotopy theory, such as Segal’s category Γ or Alain Connes’ cyclic category Λ [BM11].”
Dendroidal Segal spaces and ∞‐operads (2013, unknown): “As the category Ω is a generalized Reedy category (see [3, Example 2.8]), the model category above can be obtained as special case of [3, Theorem 1.6].”
Genuine equivariant operads (2017, background): “However, our arguments are more subtle than those in [2], which need no analogue of the FG families.”
On the equivalence between Lurie's model and the dendroidal model for infinity-operads (2013, background): “The previous lemma in fact shows that, like Ω, the category Φ is a dualizable generalized Reedy category in the sense of [8].”
The Frobenius condition, right properness, and uniform fibrations (2015, background): “m {a,b} → {x,y} that sends x to a∧b and y to a∨b is neither an isomorphism nor does it factor through 1; hence, the cube category in this case is not even a generalized Reedy category in the sense of [3]. UNIFORM FIBRATIONS AND THE FROBENIUS CONDITION 5 Example1.5 (Functorial cylinder in cubical set”
Homotopy Theory of Higher Categories: THE MODEL STRUCTURE (2010, background): “This is closely related to the corresponding result for diagrams over a Reedy category, see for example Barwick [17] and Berger-Moerdijk [32].”