Is there any further reference besides "Basic Concepts of Enriched Categories" (Kelly) for completion under T-(weighted) limits/colimits? (in which T is a set of weights)
Thank you in advance
$\begingroup$
$\endgroup$
3
-
1$\begingroup$ What are F-(weighted) limits? $\endgroup$– David Roberts ♦Commented Jul 14, 2015 at 13:48
-
1$\begingroup$ What does "F" refer to? I don't recall F-categories appearing in Kelly's book. Do you simply mean that you're interested in limits / colimits weighted by a (co)presheaf? If so, are you interested in the enriched case? $\endgroup$– Tim CampionCommented Jul 14, 2015 at 13:48
-
$\begingroup$ Sorry. I am aware of F-categories. But, instead, I was using a wrong notation for a set of weights. Thank you for your answer. I am going to take a look in both references. $\endgroup$– FernandoCommented Jul 15, 2015 at 5:59
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
0
An extensive study of such cocompletions (thus also their duals - completions), together with some characterisation results, is given in the paper:
"A Representation Results for Free Cocompletions" by J. Power, G.L. Cattani and G. Winskel
$\begingroup$
$\endgroup$
In the case of enriched categories, a review of the free cocompletion theory can be found in Kelly and Schmitt's Notes on Enriched Categories with colimits of some class. I believe this is a more down-to-earth perspective than Power/Cattani/Winskel's 2-categorical approach.
answered Jul 14, 2015 at 15:24