Enriched locally presentable categories - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T22:20:09Z http://mathoverflow.net/feeds/question/53470 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/53470/enriched-locally-presentable-categories Enriched locally presentable categories Martin Brandenburg 2011-01-27T09:31:49Z 2011-01-27T17:39:30Z <p>Is there a standard reference for the theory (if it exists) of $\mathcal{V}$-enriched locally presentable categories? Here $\mathcal{V}$ is a cosmos. Does anything unexpected happens here in contrast to the case $\mathcal{V}=\text{Set}$ treated in "Locally Presentable And Accessible Categories" by Adamek &amp; Rosicky? In particular I'm interested in the case $\mathcal{V} = \text{Cat}$. </p> http://mathoverflow.net/questions/53470/enriched-locally-presentable-categories/53474#53474 Answer by Steve Lack for Enriched locally presentable categories Steve Lack 2011-01-27T09:51:24Z 2011-01-27T09:51:24Z <p>The standard reference is <a href="http://archive.numdam.org/ARCHIVE/CTGDC/CTGDC_1982__23_1/CTGDC_1982__23_1_3_0/CTGDC_1982__23_1_3_0.pdf" rel="nofollow">this paper by Max Kelly</a>.</p> <p>Perhaps the most unexpected thing is how well the theory works!</p> http://mathoverflow.net/questions/53470/enriched-locally-presentable-categories/53512#53512 Answer by Karol Szumiło for Enriched locally presentable categories Karol Szumiło 2011-01-27T17:25:59Z 2011-01-27T17:39:30Z <p>The theory is also developed further in two papers by Borceux, Quinteiro and Rosický: <em>Enriched accessible categories</em> <a href="http://www.ams.org/mathscinet-getitem?mr=1419612" rel="nofollow">MR1419612</a> and <em>A theory of enriched sketches</em> <a href="http://www.ams.org/mathscinet-getitem?mr=1624638" rel="nofollow">MR1624638</a>. In the second one they say that they are particularly interested in case $\mathcal{V} = \text{Cat}$ and that they "intend to study this in a further publication", but I don't know of such a publication.</p>