# Details of talk

Title | Constellations: re-thinking composition of functions |
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Presenter | Tim Stokes (University of Waikato) |

Author(s) | Dr Tim Stokes |

Session | Algebra |

Time | 15:30:00 2016-12-05 |

Abstract | 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. |