From: Ross Street <ross.street@mq.edu.au>
To: Redi Haderi <haderiredi@gmail.com>
Cc: "categories@mta.ca list" <categories@mta.ca>
Subject: Re: Interpreting category-valued presheaves
Date: Tue, 18 Feb 2020 04:23:38 +0000 [thread overview]
Message-ID: <E1j4U7n-0002KI-Be@rr.mta.ca> (raw)
In-Reply-To: <E1j3Mmc-00089f-JN@rr.mta.ca>
Dear Redi Haderi
Max Kelly's book ``Basic concepts of enriched category theory'' generalises
this whole Kan business to V-categories for a decent base V.
So, for the case V = Cat, you obtain the result for 2-categories.
I say ``the result'', but of course, for 2-categories there are versions for
weaker structures (bicategories, pseudofunctors, and so on).
The Cat-enriched version is the strict case which you seem to want.
Regards,
Ross Street
On 16 Feb 2020, at 6:11 AM, Redi Haderi <haderiredi@gmail.com<mailto:haderiredi@gmail.com>> wrote:
Given a category C we know that the category of set-valued presheaves on C
may be interpreted as a free cocompletion of C. More precisely, if we
denote PSh(C) the presheaf category, then colimit-preserving functors from
PSh(C) to a cocomplete category D correspond to functors from C to D (via
Yoneda extension).
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2020-02-18 4:23 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-02-15 19:11 Redi Haderi
2020-02-18 4:23 ` Ross Street [this message]
[not found] ` <CAGTPUbjsjtS6i5jhJRyR59OvW88Jrq7u-xC_50ntoDWzxm3n0g@mail.gmail.com>
2020-02-21 1:47 ` Ross Street
2020-02-19 11:28 ` Keith Harbaugh
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