From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Luc Pellissier <luc.pellissier@lipn.univ-paris13.fr>
Cc: categories@mta.ca
Subject: Re: Functors arising from a relational Grothendieck construction
Date: Fri, 16 Jun 2017 15:16:57 +0200 [thread overview]
Message-ID: <E1dLsdj-0008PH-SL@mlist.mta.ca> (raw)
In-Reply-To: <E1dKwD6-0000jU-1e@mlist.mta.ca>
Dear Luc,
by a theorem of B'enabou (and R. Street independently I guess)
functors to BB correspond to lax normalized functors from BB^op to
Dist, the bicategory of distributors. (see e.g. "Distributors at Work"
on my homepage).
This equivalence restricts to one between Conduch'e fibrations over BB
and normalized pseudofunctors from BB^op to Dist.
Replacing Set by 2 (i.e. {\emptyset,{\emptyset}}) and restricting to
discrete guys functors from BB^op to Rel are equivalent to Conduch'e
fibrations over BB which are faithful and reflect identities.
In this case the Conduch'e condition amounts to a unique lifting
property of factorization from the base tot he total category.
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2017-06-16 13:16 UTC|newest]
Thread overview: 7+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-06-12 9:37 Luc Pellissier
2017-06-14 1:41 ` David Yetter
2017-06-16 13:16 ` Thomas Streicher [this message]
2017-06-17 5:02 ` Ross Street
2017-06-17 9:27 ` Thomas Streicher
2017-06-23 13:56 ` Luc Pellissier
[not found] ` <5B931A70-3299-433D-89AC-7DFA8627CC2B@lipn.univ-paris13.fr>
2017-06-24 8:37 ` Thomas Streicher
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