[ALGTOP-L] Internal Category References
kock at imf.au.dk
Wed Mar 17 06:08:44 EDT 2010
Philip Hackney wrote:
> Is there a good general reference for internal category theory?
> Also, is there a way to get from enriched to internal categories, or
> vice versa? If you can't do this in general, are there reasonable
> examples where you can?
> --Philip Hackney
The notion of internal category was studied already in the 1950s in
France (Grothendieck, Ehresmann), mainly in terms of simplicial objects
with certain properties (the _nerve_ of the internal category).
A concise account is in Johnstone's "Topos Theory", Chapter 2 (1977)
As for the second question, these issues are best considered through the
comprehensive notion of indexed, or fibered, category, see again "Topos
Theory" (Appendix on Locally Internal Categories).
A more elaborate text is Chapter B.2 in Johnstone's "Sketches of an
More information about the ALGTOP-L