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A model for the homotopy theory of homotopy theory

- C. Rezk
- Mathematics
- 6 November 1998

We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, “functors between two homotopy theories form a homotopy theory”, or more… Expand

Spaces of algebra structures and cohomology of operads

- C. Rezk
- Mathematics
- 1996

The aim of this paper is two-fold. First, we compare two notions of a "space" of algebra structures over an operad A: 1. the classification space, which is the nerve of the category of weak… Expand

Simplicial structures on model categories and functors

- C. Rezk, S. Schwede, B. Shipley
- Mathematics
- 19 January 2001

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories… Expand

A cartesian presentation of weak n–categories

- C. Rezk
- Mathematics
- 23 January 2009

We propose a notion of weak (n+k,n)-category, which we call (n+k,n)-Theta-spaces. The (n+k,n)-Theta-spaces are precisely the fibrant objects of a certain model category structure on the category of… Expand

An ∞‐categorical approach to R‐line bundles, R‐module Thom spectra, and twisted R‐homology

- M. Ando, C. Rezk, A. Blumberg, David Gepner, M. Hopkins
- Mathematics
- 18 March 2014

We develop a generalization of the theory of Thom spectra using the language of ∞‐categories. This treatment exposes the conceptual underpinnings of the Thom spectrum functor: we use a new model of… Expand

Notes on the Hopkins-Miller theorem

- C. Rezk
- Mathematics
- 1998

We give an exposition of the proof of a theorem of Hopkins and Miller, that the spectra En admit an action of the Morava stabilizer group.

Units of ring spectra and Thom spectra

- M. Ando, A. Blumberg, David Gepner, M. Hopkins, C. Rezk
- Mathematics
- 24 October 2008

We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. We recall (from May, Quinn, and Ray) that a commutative ring spectrum A has a spectrum of units… Expand

The units of a ring spectrum and a logarithmic cohomology operation

- C. Rezk
- Mathematics
- 1 July 2004

Recall that if R is a commutative ring, then the set R× ⊂ R of invertible elements of R is naturally an abelian group under multiplication. This construction is a functor from commutative rings to… Expand

The congruence criterion for power operations in Morava $E$-theory

- C. Rezk
- Mathematics
- 14 February 2009

We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson's congruence criterion for torsion free lambda-rings. In addition, we provide a… Expand

Topological Modular Forms of Level 3

- M. Mahowald, C. Rezk
- Mathematics
- 10 December 2008

We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the "building complex" associated to level 3 structures at the prime 2.… Expand

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