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# Details of talk

Title Constellations: re-thinking composition of functions Tim Stokes (University of Waikato) Dr Tim Stokes Algebra 15:30:00 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 $g$. \medskip 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. \medskip We show: \begin{itemize} \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. \end{itemize} This is joint work with Victoria Gould.