Cat as a closed model category
R. W. Thomason (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Displaying similar documents to “Simplicial approximation.”
Cat as a closed model category
Kan fibrations in the category of simplicial spaces
R. Seymour (1980)
Fundamenta Mathematicae
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Simplicial groups as models for -types
J. G. Cabello (1997)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Loop spaces of the Q-construction
A. Neeman (2000)
Fundamenta Mathematicae
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Giffen in [1], and Gillet-Grayson in [3], independently found a simplicial model for the loop space on Quillen's Q-construction. Their proofs work for exact categories. Here we generalise the results to the K-theory of triangulated categories. The old proofs do not generalise. Our new proof, aside from giving the generalised result, can also be viewed as an amusing new proof of the old theorems of Giffen and Gillet-Grayson.
The Lusternik-Schnirelman categories of a product space
Floris Takens (1970)
Compositio Mathematica
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Homotopy colimits and cohomology with local coefficients
M. Bullejos, E. Faro, M. A. García-Muñoz (2003)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A simplicial description of the homotopy category of simplicial groupoids.
Garzon, A.R., Miranda, J.G., Osorio, R. (2000)
Theory and Applications of Categories [electronic only]
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Cochains and homotopy type
Michael A. Mandell (2006)
Publications Mathématiques de l'IHÉS
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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E algebras is faithful but not full.
Coherent prohomotopy theory
Timothy Porter (1978)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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