From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10030 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: Joseph Moeller Newsgroups: gmane.science.mathematics.categories Subject: tensor of cocomplete categories Date: Thu, 24 Oct 2019 19:45:18 -0700 Message-ID: Reply-To: Joseph Moeller Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="211353"; mail-complaints-to="usenet@blaine.gmane.org" To: categories@mta.ca Original-X-From: majordomo@rr.mta.ca Fri Oct 25 16:39:34 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1iO0kX-000smA-Fe for gsmc-categories@m.gmane.org; Fri, 25 Oct 2019 16:39:33 +0200 Original-Received: from rr.mta.ca ([198.164.44.159]:33230) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1iO0iO-0004UM-PN; Fri, 25 Oct 2019 11:37:20 -0300 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1iO0iD-0000QZ-FZ for categories-list@rr.mta.ca; Fri, 25 Oct 2019 11:37:09 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:10030 Archived-At: Hello category theorists, I've been working with tensor products of categories of various degrees of cocompletion. What I mean is that I'm considering categories which are J-cocomplete for some class of small categories J, that is it has all colimits of diagrams for all shapes in J. I know that Kelly gives a tensor product for such things when J is small in section 6.5 of his book on Enriched Category Theory, but I'm working with large J, including when J has all categories, and then we're talking about cocomplete categories. I think these things must have been considered somewhere, and I'm hoping you can help me find a reference. Joe Moeller (He/Him) Graduate Student, Mathematics Department University of California, Riverside [For admin and other information see: http://www.mta.ca/~cat-dist/ ]