Convergence and quantale-enriched categories

Approximation in quantale-enriched categories

Our work is a foundational study of the notion of approximation inQ-categories and in (U,Q)-categories, for a quantale Q and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Qand (U,Q)-categories. We fully characterize continuous Q-categories (resp. (U,Q)-categories) among all cocomplete Q-categories (...

Restriction categories as enriched categories

Article history: Received 27 November 2012 Received in revised form 4 September 2013 Accepted 20 December 2013 Communicated by B.P.F. Jacobs

Enriched Indexed Categories

We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V . This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases. We then describe the appropriate notion of “limit” for such enriched indexed categories, and show that th...

Enriched Categories , Internal Categories and Change of Base Dominic Verity