1998
DOI: 10.1016/s0022-4049(97)00075-3
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On the equivariant 2-type of a G-space

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Cited by 4 publications
(8 citation statements)
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“…Our definitions differ slightly from those found in those references in the sense that we put special emphasis in the groupoid fibre of a torsor. This is closer to the way torsors are defined and used, for example, in [9].…”
Section: A 2-torsors and Cotriple Cohomologymentioning
confidence: 83%
See 3 more Smart Citations
“…Our definitions differ slightly from those found in those references in the sense that we put special emphasis in the groupoid fibre of a torsor. This is closer to the way torsors are defined and used, for example, in [9].…”
Section: A 2-torsors and Cotriple Cohomologymentioning
confidence: 83%
“…The objects in Crs n are homotopy n-types, that is, they have trivial "homotopy groups" in dimensions greater than n. The homotopy groups of a crossed complex are defined as follows: π 0 (C) is the set of connected components of the base groupoid, so π 0 (C) = π 0 (G). Similarly, π 1 (C) = π 1 (C 2 ) = G/ im(δ 2 ), the fundamental groupoid of the base crossed module of C. For n 2, π n (C) is defined as the "homology group" H n (C) : π 1 (C) → Ab of the induced chain complex of π 1 (C)-modules (9). Note that if we consider π n (C) as a G-module via the canonical projection q : G → π 1 (C), for n 2, the G-crossed module (π n (C), 0) is the kernel of the induced map ∂ n : C n / im(∂ n+1 ) → C n−1 (see (10) below).…”
Section: Crossed Complexes and Their Postnikov Towersmentioning
confidence: 99%
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“…This should not be confused with the stronger notion of weak equivariant-homotopy equivalence, which is a equivariant pointed map that induces weak homotopy equivalences on the fixed point subspaces of all subgroups of Γ. The Postnikov invariant of a equivarianthomotopy 2-type is not an element of a cohomology group H 3 Γ (G, A) as above, but rather an element of a Bredon-Moerdijk-Svensson 3-rd cohomology groups [3,14], as it is showed in [4].…”
Section: Introductionmentioning
confidence: 98%