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Indexed Categories and Their Applications (Lecture Notes in Mathematics)
Indexed Categories and Their Applications (Lecture Notes in Mathematics)
Date: 03 June 2011, 00:23

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The recent development of the theory of indexed categories has its origins in the programme, first proposed by F.W. Lawvere, of learning how to develop familiar mathematical notions over an arbitrary base topos in order to remove their dependence, on classical set theory. This programme has already led to great advances in our understanding of continuously variable structures (sheaves, bundles, etc.) and their relation to the corresponding constant structures. However, in order to develop category theory itself in this way, it was realized that one needed to develop a notion of "family of objects (or morphisms) indexed by a variable set (= an object of the base topos)", and a suitably flexible technique for handling such indexed families.

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