SUO: Re: Re: Enchoiry on Colimits and Diagrams of Theories
----- Original Message -----
From: "Robert E. Kent" <rekent@ontologos.org>
To: "Jon Awbrey" <jawbrey@oakland.edu>
Cc: "SUO" <standard-upper-ontology@ieee.org>
Sent: Saturday, June 28, 2003 9:40 AM
Subject: SUO: Re: Enchoiry on Colimits and Diagrams of Theories
> are constructed over such "discrete" graphs (no edges). In Set, a pair of
> functions that share source and target sets
> A1 --f1, f2--> A2
> is a diagram whose shape or indexing graph has two nodes {n1, n2} and two
> edges {e1, e2}, with both edges linking n1 to n2. The colimit of this
> diagram is called the coequalizer of the "projection" function
> p : A2 --> A2/E
> on the quotient set of A2 by the equivalence relation E \subset A2xA2
> generated by the endorelation {(f1(a1), f2(a1)) | for a1 in A1}.
Should read:
The colimit of this diagram is called the coequalizer -- it consists of the
"canonical surjection" function
p : A2 --> A2/E : a2 |--> [a2]
from the set A2 to the quotient set A2/E of A2 by the equivalence relation E
\subset A2xA2 generated by the endorelation {(f1(a1), f2(a1)) | for a1 in
A1}.
Furthermore, the notion of *endorelation* and *quotient* that is used to
construct various colimits in Set, faithfully translates up to the
categories of FOL languages and theories.
Robert E. Kent
rekent@ontologos.org