Date: Mon, 14 Nov 1994 17:17:32 +0400 (GMT+4:00)
From: categories <cat-dist@mta.ca>
Subject: papers on internal categories ???

Date: Mon, 14 Nov 1994 17:55:48 +0100 (MET)
From: Wojciech Zaborowski <wojciech@bull.mimuw.edu.pl>

Hi everyone in 'categories' !

I found only a few pages related in Johnstone's Topos theory'.
I am interested in serious introduction to 'internal categories'.
I am especially looking for:
 1: full systematic internalization of all fundamental concepts of category
    theory, including natural transformations, limits and adjoints
 2: books, papers etc. developing classic theories on such abstract (internal)
    level
Does anyone enjoy playing with 'internal' too ?

Date: Mon, 14 Nov 1994 18:41:38 -0400 (AST)
From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: papers on internal categories ???

Date: Tue, 15 Nov 1994 08:54:47 +1100
From: Ross Street <street@macadam.mpce.mq.edu.au>

>I am interested in serious introduction to 'internal categories'.

Ross Street, Cosmoi of internal categories, Transactions American
Math. Soc. 258 (1980) 271-318; MR82a:18007

could be of interest.

--Ross

Date: Tue, 15 Nov 1994 10:24:49 -0400 (AST)
From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: papers on internal categories ???

Date: 15 Nov 1994 14:00:52 GMT
From: cxm7@po.cwru.edu


> Date: Mon, 14 Nov 1994 17:55:48 +0100 (MET)
> From: Wojciech Zaborowski <wojciech@bull.mimuw.edu.pl>
>
> Hi everyone in 'categories' !
>
> I found only a few pages related in Johnstone's Topos theory'.
> I am interested in serious introduction to 'internal categories'.
> I am especially looking for:
>  1: full systematic internalization of all fundamental concepts of category
>     theory, including natural transformations, limits and adjoints
>  2: books, papers etc. developing classic theories on such abstract (internal)
>     level
> Does anyone enjoy playing with 'internal' too ?
>
        There is a lot in Johnstone's few pages. I also cover this, making
it look as much like naive category theory as I could, in chapter 20
of my book _Elementary categories, elementary toposes_ (Oxford 1992).
This book is due out in paperback soon.

        And you should look at Benabou "Fibred categories and the
foundations of naive category theory" (Jour. Symbolic Logic 50,
1985, 10-37) and Johnstone and Pare _Indexed categories_, Springer
Lecture Notes in Math 661.

Colin McLarty