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Details of talk

TitleConstellations: re-thinking composition of functions
PresenterTim Stokes (University of Waikato)
Author(s)Dr Tim Stokes
Time15:30:00 2016-12-05

Constellations are partial algebras that are one-sided generalisations of
categories.  Categories model classes of objects together with suitably defined
mappings between them.  Each mapping, or arrow, has a domain and codomain
(source and target), and composition of mappings $f\cdot g$ is defined precisely
when the codomain of $f$ coincides with the domain of $g$.

An alternative notion of composition arises if one only requires the image (not
codomain) of $f$ to be a {\em subset} of the domain of $g$.  When this is done,
precise information about codomains is no longer needed, and ``arrows" have
sources but no targets.  This is more natural in many examples.  The abstract
concept corresponding to the concrete examples is that of a constellation.

We show:
\item  categories are precisely two-sided constellations;
\item the naive notion of substructure can be captured within constellations
but not within categories;
\item by virtue of a straightforward construction, many familiar concrete
categories may be constructed from natural constellations that are in fact
quotients of the corresponding categories.  
This is joint work with Victoria Gould.