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From: ptj@maths.cam.ac.uk
To: Steve Vickers <s.j.vickers@cs.bham.ac.uk>
Cc: "categories@mta.ca list" <categories@mta.ca>
Subject: Re: Direct image functors
Date: 08 Nov 2022 21:36:12 +0000	[thread overview]
Message-ID: <E1osxL2-0000jC-FG@rr.mta.ca> (raw)
In-Reply-To: <1C2D2A4F-AFE4-4285-A70A-A77888CFB934@cs.bham.ac.uk>

Dear Steve,

> By the way, I looked at the Elephant to see what you said there, and I
> saw "we shall see later that, in a sense, f_* 'embodies the geometric
> aspects' of the morphism f". What did you have in mind for the "we shall
> see later"?
>
I'm not now sure exactly what I meant, but I believe I was thinking
primarily of the fact that f_*: Sh(X) --> Sh(Y) points in the same
direction as a continuous map f: X --> Y of spaces. On the other hand,
my assertion that f^* `embodies the algebraic aspects' of f is certainly
explained by A4.1 18 -- the fact that inverse image functors are unital
morphisms of geometric allegories.

Peter


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


       reply	other threads:[~2022-11-08 21:36 UTC|newest]

Thread overview: 5+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
     [not found] <1C2D2A4F-AFE4-4285-A70A-A77888CFB934@cs.bham.ac.uk>
2022-11-08 21:36 ` ptj [this message]
2022-11-08 14:10 Steve Vickers
2022-11-10 11:03 ` George Janelidze
  -- strict thread matches above, loose matches on Subject: below --
2022-11-07 10:56 Steve Vickers
2022-11-08 10:46 ` ptj

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