Morphisms of diagrams

[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.

By the way, Barr in SLN 236 (page 52) defines an entirely
different notion of morphism of diagrams which Tholen and Tozzi
develop extensively in "Completions of Categories and Initial
Completions", Cahiers 1989, pages 127-156.  This makes Lim a
covariant functor.



Charles Wells, 105 South Cedar Street, Oberlin, Ohio 44074, USA.
(I am on sabbatical until 20 August 1997 and cannot easily be reached
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