# Details of talk

Title | Presheaves over join restriction categories |
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Presenter | Daniel Lin (Macquarie University) |

Author(s) | Mr Daniel Lin |

Session | Category Theory, Algebraic Topology, K-Theory |

Time | 17:00:00 2017-12-13 |

Abstract | Restriction categories were first introduced in the early 1990s and later studied in the early 2000s as a means of generalising the notion of a partial map category; the idea being to capture the partiality of each map through a corresponding idempotent on its domain, called a restriction idempotent. As it turns out, the hom-sets of any restriction category has a natural partial ordering, and this, together with the notion of compatibility, gave rise to the notion of a join restriction category. In this talk, we shall see that every join restriction category may be freely completed to a cocomplete join restriction category, given by the partial map category of sheaves on some site. However, we shall also see that every join restriction category has a free cocompletion equivalent to this partial map category of sheaves. This equivalent category takes a simpler form, with join restriction presheaves as its objects. |