The homotopy axiom in semialgebraic cohomology.
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Théories cohomologiques.
Henri Cartan (1976)
Inventiones mathematicae
Topos based homology theory
M. V. Mielke (1993)
Commentationes Mathematicae Universitatis Carolinae
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. The...
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