Re: monic epics

[Lawrence Stout <lstout@iwu.edu>]

The Goguen category of L-fuzzy sets on a lattice L (Objects are pairs
(A,\alpha) where \alpha:A\to L and morphisms are functions f:A\to B
such that \beta{f(a)) >= \alpha(a)) has all functions whose
underlying set function is an isomorphism both epic and monic, but
not, in general, isomorphisms, which must preserve the lattice valued
membership on the nose.  Since these monic, epic maps are the ones
which give the right subobjects to consider for fuzzy logic they are
of interest.  They do not determine a "folding" like the one you
describe.


On Mar 6, 2007, at 7:11 PM, David Karapetyan wrote:

>  So does every monic, epic arrow determine such a
> "folding" or are there monic, epics that can't be characterized in
> such
> a way?
>
>



Lawrence Stout
Professof of Mathematics
Illinois Wesleyan University