## 17 Citations

### Reedy categories and the $\Theta$-construction

- Mathematics
- 2011

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

- Mathematics
- 2012

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

- Mathematics
- 2010

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

- MathematicsJournal of Topology
- 2018

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…

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

- Mathematics
- 2013

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…

### On an extension of the notion of Reedy category

- Mathematics
- 2011

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…

### Reedy categories and their generalizations

- Mathematics
- 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…

### Smoothness in Relative Geometry

- Mathematics
- 2008

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…

## References

SHOWING 1-10 OF 10 REFERENCES

### Hochschild and cyclic homology via functor homology

- Mathematics
- 2002

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

- Mathematics
- 1989

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

- Mathematics
- 2008

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

- MathematicsElements 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

- Mathematics
- 2003

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