# Reedy categories and their generalizations

@article{Shulman2015ReedyCA, title={Reedy categories and their generalizations}, author={Michael Shulman}, journal={arXiv: Algebraic Topology}, year={2015} }

We observe that the Reedy model structure on a diagram category can be constructed by iterating an operation of "bigluing" model structures along a pair of functors and a natural transformation. This yields a new explanation of the definition of Reedy categories: they are almost exactly those small categories for which the category of diagrams and its model structure can be constructed by iterated bigluing. It also gives a consistent way to produce generalizations of Reedy categories, including… Expand

#### 7 Citations

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This note explores the algebraic perspective on the notion of generalized Reedy category introduced by Berger and Moerdijk [BM08]. The aim is to unify inductive arguments by means of a canonical… Expand

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We construct a new model category presenting the homotopy theory of presheaves on "inverse EI $(\infty,1)$-categories", which contains universe objects that satisfy Voevodsky's univalence axiom. In… Expand

$(\infty,1)$-Categorical Comprehension Schemes.

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In this paper we define and study a notion of comprehension schemes for cartesian fibrations over $(\infty,1)$-categories, generalizing Johnstone's respective notion for ordinary fibered categories.… Expand

On bifibrations of model categories

- Mathematics, Computer Science
- ArXiv
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Using this Grothendieck construction for model structures, the traditional definition of Reedy model structures is revisited, and possible generalizations are revisit, and exhibit their bifibrational nature. Expand

First-Order Logic with Isomorphism

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The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on… Expand

Finite Inverse Categories as Signatures

- Mathematics, Computer Science
- ArXiv
- 2017

A simple dependent type theory is defined and it is proved that its well-formed types correspond exactly to finite inverse categories. Expand

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