The branching nerve of HDA and the Kan condition.
Gaucher, Philippe (2003)
Theory and Applications of Categories [electronic only]
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Gaucher, Philippe (2003)
Theory and Applications of Categories [electronic only]
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Gaucher, Philippe (2001)
Theory and Applications of Categories [electronic only]
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Everaert, T., Van der Linden, T. (2004)
Theory and Applications of Categories [electronic only]
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Daryl George (1984)
Fundamenta Mathematicae
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Barr, Michael (2005)
Theory and Applications of Categories [electronic only]
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J. Dugundji (1966)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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M. V. Mielke (1993)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects....