Enriched Reedy categories

@inproceedings{Angeltveit2006EnrichedRC,
  title={Enriched Reedy categories},
  author={Vigleik Angeltveit},
  year={2006}
}
This research was partially conducted during the period the author was employed by the Clay Mathematics Institute as a Liftoff Fellow. 

Reedy categories and the $\Theta$-construction

We use the notion of multi-Reedy category to prove that, if $\mathcal C$ is a Reedy category, then $\Theta \mathcal C$ is also a Reedy category. This result gives a new proof that the categories

Lax Diagrams and Enrichment

We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the philosophy of classical

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A bisimplicial model category that can be used to recover the algebraic K-theory for any Waldhausen subcategory of a model category is produced.

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Reedy categories and the $$\varTheta $$-construction

We use the notion of multi-Reedy category to prove that, if $$\mathcal C $$ is a Reedy category, then $$\varTheta \mathcal C $$ is also a Reedy category. This result gives a new proof that the

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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

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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

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In [TVa], Bertrand Toen and Michel Vaquie defined a scheme theory for a closed monoidal category (C,⊗, 1). In this article, we define a notion of smoothness in this relative (and not necessarily

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BASIC CONCEPTS OF ENRICHED CATEGORY THEORY

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Although numerous contributions from divers authors, over the past fifteen years or so, have brought enriched category theory to a developed state, there is still no connected account of the theory,

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E-mail address: vigleik@math.uchicago.edu URL: http://www.math.uchicago.edu/∼vigleik License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

  • E-mail address: vigleik@math.uchicago.edu URL: http://www.math.uchicago.edu/∼vigleik License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

Reprint of the 1982 original [Cambridge Univ. Press, Cambridge; MR0651714

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