Re: Morphisms of diagrams

[categories <cat-dist@mta.ca>]

Date: Thu, 20 Mar 1997 14:53:31 +1100 (EST)
From: Steve Lack <stevel@maths.su.oz.au>

> Date: Tue, 18 Mar 1997 11:24:35 -0400 (AST)
> From: categories <cat-dist@mta.ca>
> 
> Date: Tue, 18 Mar 1997 10:20:19 -0500
> From: Charles Wells <charles@freude.com>
> 
> Let C be a category and I and I' graphs (or categories if
> you prefer).  Define a morphism of diagrams
> psi:(delta:I-->C)-->(delta':I'-->C) to be a graph morphism (or
> functor if you prefer) psi:I-->I' together with a natural
> transformation alpha:delta' o psi-->delta.  This definition
> turns Lim into a contravariant functor from the category of
> diagrams to C (when C is complete, anyway).
> 
> I believe this construction has been familiar since the early
> days of category theory, but I don't know a reference and would
> be glad to learn of any.

The dual construction (i.e. for colimits) appears in
	Rene Guitart, ``Remarques sur les machines et les
	structures'', Cahiers XV-2 (1974);
and its sequel
	Rene Guitart and Luc Van den Bril, ``Decompositions
	et lax-completions'', Cahiers XVIII-4 (1977);
where further references are also given.

Steve Lack.