Page 1 Number 383 Alex Heller Homotopy theories Memoirs of the American Mathematical
Society Providence. Rhode Island USA January 1988 . Volume 71 : Number 383 (end of volume) …

In a previous paper, we lifted Charles Rezk's complete Segal model structure on the
category of simplicial spaces to a Quillen equivalent one on the category of “relative …

In this paper we prove that for any simplicial set $ B $, there is a Quillen equivalence
between the covariant model structure on $\mathbf {S}/B $ and a certain localization of the …

The genesis of this paper lies in the proof in [20] that the nerve functor carries lax colimits in
the category Cat of small categories to homotopy colimits in the category. X of simplicial sets …

In [19] simple conditions on “categorical simplices” are given so that, up to homotopy, the
only reasonable assignment of a (semi-) simplicial set to a small category is the standard …

We construct a cofibrantly generated Quillen model structure on the category of small n–fold
categories and prove that it is Quillen equivalent to the standard model structure on the …

We investigate cohomology and homology theories of categories with general coefficients
given by functors on simplex categories first studied by Thomason. These generalize Baues …

In this paper we show that, up to homotopy, the only" reasonable" functor which assigns a
CW complex to every small category is the classifying space construction. This result is part …

Cat 1-groups and crossed modules are equivalent formulations of 2-groups (a
twodimensional generalisation of the concept of group). A linear representation of the cat 1 …

Extending constructions by Gabriel and Zisman, we develop a functorial framework for the
cohomology and homology of simplicial sets with very general coefficient systems given by …