From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3720 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Full and faithful Date: Tue, 3 Apr 2007 22:31:54 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019482 9982 80.91.229.2 (29 Apr 2009 15:38:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:38:02 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Wed Apr 4 10:53:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Apr 2007 10:53:29 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HZ5r9-0001wr-FF for categories-list@mta.ca; Wed, 04 Apr 2007 10:48:59 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:3720 Archived-At: Perhaps "representably fully faithful" is a good name. In Cat, they are the fully faithful functors. In V-Cat they may not be fully faithful V-functors: see (with R.F.C. Walters) Yoneda structures on 2-categories, J. Algebra 50 (1978) 350-379 Also see (with A. Carboni, S. Johnson and D. Verity) Modulated bicategories, J. Pure Appl. Algebra 94 (1994) 229-282 ---Ross On 31/03/2007, at 3:44 AM, Robin Houston wrote: > A functor F: C -> D is full and faithful just when, for all > categories X and functors G, H: X -> C, the whiskering action of F > induces a bijection between [G, H] and [FG, FH] (where [G, H] > denotes the set of natural transformations from G to H). > > Clearly this formulation makes sense in any bicategory. Is there a > name for 1-cells with this property?