From: David Roberts <droberts.65537@gmail.com>
To: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
Cc: "categories@mta.ca list" <categories@mta.ca>
Subject: Re: Cartesian morphism ~~> fibration
Date: Thu, 21 Sep 2017 19:52:03 +0930 [thread overview]
Message-ID: <CAFL+ZM-TyEL0muNNjhQrpAqSEkmRaeensKtwHz1ETExTC=5eTg@mail.gmail.com> (raw)
In-Reply-To: <20170921094659.GB10551@mathematik.tu-darmstadt.de>
In fact there's a more general construction, recorded in the Stacks Project
https://stacks.math.columbia.edu/tag/08NF
and in the case that the codomain (only!) is fibred in groupoids it shows
that any cartesian functor factors as an equivalence of fibrations followed
by a fibration.
Regards,
David
On 21 Sep. 2017 7:17 pm, "Thomas Streicher" <
streicher@mathematik.tu-darmstadt.de> wrote:
>> So I guess this extends your example where the codomain is a discrete
>> fibration, merely having to replace the domain by an equivalent category.
>> This makes the original cartesian functor a Street fibration, I believe.
>
> Indeed every functor F between groupoids is a Street fibration and thus
> equivalent to a Grothendieck fibration in the sense that there is a
> fibarion P and an equivalence E such that F = PE.
>
> Interesting that this extends to fibered functors!
>
> Thomas
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2017-09-21 10:22 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-09-20 11:23 David Roberts
2017-09-20 17:49 ` Thomas Streicher
[not found] ` <20170920174906.GE8154@mathematik.tu-darmstadt.de>
2017-09-20 22:11 ` David Roberts
[not found] ` <20170921094659.GB10551@mathematik.tu-darmstadt.de>
2017-09-21 10:22 ` David Roberts [this message]
[not found] <CAFL+ZM87_oCKWjnyGcf3KqWzwoKxxf-9YDAHzzx8tV_wisoqyQ@mail.gmail.com>
2017-09-21 9:46 ` Thomas Streicher
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