Date: Wed, 30 Oct 1996 15:37:24 -0400 (AST)
Subject: Monads and Generic Subobjects

Date: Wed, 30 Oct 1996 13:52:58 -0500 (EST)
From: rmcgrail@picasso.cslab.wesleyan.edu

Hi,
        I have need for the following:
Given a category C with monad (T,unit,joint) with monic unit, and given A
in |C|, construct a category C' with C as a full subcategory and a new
almost-generic subobject X->A (never an iso and all pullbacks of X->A
along all arrows from the image of C exist) such that (T,unit,join)
extends to a monad (T',unit',join') on C'.

        I believe I have such an animal (simply a filtered colimit of a
sequence of the form C(A)->C(TA)->C(T^2(A))->..., where C(T^i(A)) extends
C with a generic subobject with target T^i(A), a la Cats and Alligators).
However, the more I stare at this construction the more I believe I am
reinventing the wheel.  Has this been done before?

--Regards
Bob McGrail

----------------------------------------------------------
rmcgrail@math.wesleyan.edu
http://www.cs.wesleyan.edu/Math/Grads/rmcgrail