From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/595 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Combining monads Date: Fri, 16 Jan 1998 14:20:24 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017061 26415 80.91.229.2 (29 Apr 2009 14:57:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:41 +0000 (UTC) To: categories Original-X-From: cat-dist Fri Jan 16 14:20:51 1998 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA25809; Fri, 16 Jan 1998 14:20:24 -0400 (AST) Original-Lines: 40 Xref: news.gmane.org gmane.science.mathematics.categories:595 Archived-At: Date: Thu, 15 Jan 1998 23:21:27 +0100 From: Jan Juerjens > > Date: Wed, 14 Jan 1998 16:21:51 +0000 (GMT) > From: Tom Leinster > > > Is the pullback of a monadic functor along a monadic functor > necessarily monadic? > Is the diagonal of the pullback square monadic? > Does this work if your restrict yourself to, say, finitary monadic > functors? > > (E.g. it works for finitary monads on Set: the theory of sets with > both ring and lattice structure (not interacting in any particular > way) comes from a monad.) > > Thanks, > Tom Leinster > Hi Tom, if I'm not mistaken, this reduces for full isomorphism-closed embeddings to the (finite) Intersection Problem (of full iso-closed subcategories) answered negatively by Trnkova, Adamek, Rosicky ("Topological reflections revisited", ProcAMS 108,3 (1990) p605; see also Tholen "Reflective Subcategories" TopAppl 27 (1987) p201, Adamek, Rosicky "Intersections of reflective subcategories" ProcAMS 103 (1988) p710). Full iso-closed subcategories of locally lambda-presentable categories are reflective and closed under lambda-directed colimits iff they are lambda-orthogonal, so intersections of such subcategories are reflective (Adamek, Rosicky "Locally presentable and Accessible Categories" CUP 94). Bye, Jan [ + thanks again for the supervisions ... :-) ]