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

Reedy categories and the Θ -construction

We use the notion of multi-Reedy category to prove that, if C is a Reedy category, then Θ C is also a Reedy category. This result gives a new proof that the categories Θ n are Reedy categories. We

Higher descent data as a homotopy limit

We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial

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

On modified Reedy and modified projective model structures

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

An algebraic model for rational torus‐equivariant spectra

We provide a universal de Rham model for rational G ‐equivariant cohomology theories for an arbitrary torus G . More precisely, we show that the representing category, of rational G ‐spectra, is

On an extension of the notion of Reedy category

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

Commutative ring objects in pro-categories and generalized Moore spectra

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is

References

SHOWING 1-10 OF 10 REFERENCES

Hochschild and cyclic homology via functor homology

A description of Hochschild and cyclic homology of commutative algebras via homo- logical algebra in functor categories was achieved in (4). In this paper we extend this approach to associative

Homotopy spectral sequences and obstructions

For a pointed cosimplicial spaceX•, the author and Kan developed a spectral sequence abutting to the homotopy of the total space TotX•. In this paper,X• is allowed to be unpointed and the spectral

Topological Hochschild homology and cohomology of A∞ ring spectra

Let A be an A_\infty ring spectrum. We use the description from [2] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using

BASIC CONCEPTS OF ENRICHED CATEGORY THEORY

  • G. M. Kelly
  • Mathematics
    Elements of ∞-Category Theory
  • 2005
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,

Model categories and their localizations

Localization of model category structures: Summary of part 1 Local spaces and localization The localization model category for spaces Localization of model categories Existence of left Bousfield

Math. Soc

  • Math. Soc
  • 1623

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

  • Basic concepts of enriched category theory, Repr. Theory Appl. Categ
  • 2005