From: Ross Street <street@ics.mq.edu.au>
To: Categories <categories@mta.ca>
Subject: Re: Full and faithful
Date: Tue, 3 Apr 2007 22:31:54 +1000 [thread overview]
Message-ID: <E1HZ5r9-0001wr-FF@mailserv.mta.ca> (raw)
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?
next reply other threads:[~2007-04-03 12:31 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2007-04-03 12:31 Ross Street [this message]
-- strict thread matches above, loose matches on Subject: below --
2007-03-30 17:44 Robin Houston
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