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Higher topos theory
, 2006
"... Let X be a topological space and G an abelian group. There are many different definitions for the cohomology group H n (X; G); we will single out three of them for discussion here. First of all, we have the singular cohomology groups H n sing (X; G), which are defined to be cohomology of a chain com ..."
Abstract

Cited by 47 (0 self)
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Let X be a topological space and G an abelian group. There are many different definitions for the cohomology group H n (X; G); we will single out three of them for discussion here. First of all, we have the singular cohomology groups H n sing (X; G), which are defined to be cohomology of a chain complex of Gvalued singular cochains on X. An alternative is to regard H n (•, G) as a representable functor on the homotopy category
The homotopy theory of fusion systems
"... The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like pcompleted classifying spaces of finite groups. These spaces occur as the “classifying spaces ” of certain algebraic objects, which we call plocal finite groups. A plocal finite group con ..."
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Cited by 35 (10 self)
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The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like pcompleted classifying spaces of finite groups. These spaces occur as the “classifying spaces ” of certain algebraic objects, which we call plocal finite groups. A plocal finite group consists, roughly speaking, of a finite pgroup S and fusion data on subgroups of S, encoded in a way explained below. Our starting point is our earlier paper [BLO] on pcompleted classifying spaces of finite groups, together with the axiomatic treatment by Lluís Puig [Pu], [Pu2] of systems of fusion among subgroups of a given pgroup. The pcompletion of a space X is a space X ∧ p which isolates the properties of X at the prime p, and more precisely the properties which determine its mod p cohomology. For example, a map of spaces X f −− → Y induces a homotopy equivalence
Homotopy Coherent Category Theory
, 1996
"... this paper we try to lay some of the foundations of such a theory of categories `up to homotopy' or more exactly `up to coherent homotopies'. The method we use is based on earlier work on: ..."
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Cited by 22 (6 self)
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this paper we try to lay some of the foundations of such a theory of categories `up to homotopy' or more exactly `up to coherent homotopies'. The method we use is based on earlier work on:
Author address: Homotopy theory of diagrams
, 2001
"... Chapter I. Model approximations and bounded diagrams 5 ..."