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Abstract: L are simplicial sets, then there is a strong deformation retraction of the fundamental crossed complex of the cartesian product K \Theta L onto the tensor product of the fundamental crossed complexes of K and L. This satisfies various side-conditions and associativity/interchange laws, as for the chain complex version. Given simplicial sets K 0 ; : : : ; K r , we discuss the r-cube of homotopies induced on (K 0 \Theta : : : \Theta K r ) and show these form a coherent system. We introduce a... (Update)
Context of citations to this paper: More
...used to prove (3) together with: 1. additional information on the Eilenberg Zilber theorem for crossed complexes, proved by Tonks in [32]; 2. results on homotopy coherence developed by Cordier and Porter in [14] 3. general techniques of equivariant theory, as given by say...
...used to prove (3) together with: 1. additional information on the Eilenberg Zilber theorem for crossed complexes, proved by Tonks in [34]; 2. results on homotopy coherence developed by Cordier and Porter in [16] 3. general techniques of equivariant theory, as given by say...
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BibTeX entry: (Update)
Tonks, A.P, Theory and applications of crossed complexes, Ph.D. Thesis, University of Wales, Bangor, (1993). http://citeseer.ist.psu.edu/tonks93theory.html More
@misc{ tonks93theory,
author = "A. Tonks",
title = "Theory and applications of crossed complexes",
text = "Tonks, A.P, Theory and applications of crossed complexes, Ph.D. Thesis,
University of Wales, Bangor, (1993).",
year = "1993",
url = "citeseer.ist.psu.edu/tonks93theory.html" }
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31 Elements of Homotopy Theory (context) - Whitehead - 1978
27 Colimit theorems for relative homotopy groups (context) - Brown, Higgins - 1981
24 Lecture Notes in Mathematics (context) - Bousfield, Kan et al. - 1972
19 Introduction to bicategories (context) - Benabou - 1967
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16 Group-theoretic algebraic models for homotopy types (context) - Carrasco, Cegarra - 1991
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13 Natural Associativity and Commutativity (context) - MacLane - 1963
12 Limits indexed by category-valued 2-functors (context) - Street - 1976
12 the connection between the second relative homotopy groups o.. (context) - Brown, Higgins - 1978
12 The classifying space of a crossed complex (context) - Brown, Higgins - 1991
12 Combinatorial homotopy II (context) - Whitehead - 1949
11 Homotopy limits and colimits (context) - Vogt - 1973
10 Applications of perturbation theory to iterated fibrations (context) - Lambe, Stasheff - 1987
9 Resolutions for extensions of groups (context) - Wall - 1961
9 The twisted Eilenberg-Zilber theorem (context) - Brown - 1967
9 Algebraic models of 3-types and automorphism structures for .. (context) - Brown, Gilbert - 1989
8 Vogt's theorem on categories of homotopy coherent diagrams (context) - Cordier, Porter - 1986
6 A general formulation of homotopy limit (context) - Bourn, Cordier - 1989
6 Homotopy colimits in the category of small categories (context) - Thomason - 1979
5 Homologie des espaces fibr'es (context) - Shih - 1962
5 the Van Kampen Theorem (context) - Artin, Mazur - 1966
4 Two constructions on lax functors (context) - Street - 1972
4 Simplicial localizations of categories (context) - Dwyer, Kan - 1980
3 Pure and Appl (context) - Brown, Higgins et al. - 1987
3 groupoids and homotopy types (context) - Kapranov, Voevodsky - 1991
3 Sur les limites homotopiques de diagrammes homotopiquement c.. (context) - Cordier - 1987
2 The algebra of oriented simplices (context) - Street - 1989
2 Pullback functors and crossed complexes (context) - Howie - 1979
2 fold extensions of groups and cohomology (context) - Huebschmann - 1980
1 crossed complexes and classifying spaces (context) - Brown, Golasi'nski et al. - 1993
1 Porter From simplicial groupoids to crossed complexes (context) - Ehlers - 1992
1 Pure and Appl (context) - Gray, lax et al. - 1980
1 Tensor products of 1-categories (context) - Steiner
1 Simplicial sets and weak n-groupoids (context) - Golasi'nski
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