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Tensor topology

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If you have a question about this talk, please contact Dr Steve Vickers.

[Pau, visiting here for two weeks, will report on some of his PhD work with Chris Heunen.]

In categories of Hilbert bundles, Hilbert modules and sheaves over a topological space, the open subsets of the base space can be algebraically recovered via so-called idempotent subunits. These subunits provide any braided monoidal category with a built-in notion of space, and form a meet-semilattice that corresponds to different intuitions in different categories (e.g. truth values in the context of logic and side-effect-free observations in the context of order theory).

We introduce a notion of support that captures ‘where morphisms happen’ and that is characterised by a universal property. There are also appropriate notions of localisation (to a region of space) and of causal structure. The goal of this talk is to introduce these concepts and their main theoretical properties, as well as to discuss potential applications to categorically modelling concurrent programs and modal logics.

Joint work with Chris Heunen and Sean Tull.

This talk is part of the Lab Lunch series.

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