T-homotopy and refinement of observation. IV. Invariance of the underlying homotopy type.
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...
Dans cet article, on construit une résolution injective explicite des puissances symétriques tordues dans la catégorie des foncteurs strictement polynomiaux. Cette construction généralise à toute caractéristique la construction donnée par Friedlander et Suslin en caractéristique 2.
The aim of this article is to bring together various themes from fairly elementary homotopy theory and to examine them, in part, from a historical and philosophical viewpoint.