Simplicial and categorical diagrams, and their equivariant applications.
Fritsch, Rudolf, Golasiński, Marek (1998)
Theory and Applications of Categories [electronic only]
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Displaying similar documents to “On three types of simplicial objects”
Simplicial and categorical diagrams, and their equivariant applications.
Coherent prohomotopy theory
Timothy Porter (1978)
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.
Fibrations and classifying spaces : an axiomatic approach I
Peter I. Booth (1998)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Cat as a closed model category
R. W. Thomason (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A suspension theorem for the proper homotopy and strong shape theories
C. Elvira-Donazar, L. J. Hernandez-Paricio (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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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.
Simplicial Sets from Categories.
D.M. Latch, R.W. Thomason, W.S. Wilson (1978/79)
Mathematische Zeitschrift
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Heaps and unpointed stable homotopy theory
Lukáš Vokřínek (2014)
Archivum Mathematicum
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In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty.