University of Birmingham > Talks@bham > Theoretical computer science seminar > Geometric morphisms as structure preserving maps and other nice characterisations

Geometric morphisms as structure preserving maps and other nice characterisations

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If you have a question about this talk, please contact Benedikt Ahrens.

Geometric morphisms, the ‘correct’ arrows between toposes, can be represented as adjunctions between categories of locales over toposes. Categories of locales can be axiomatised using the double power locale monad, so it is pleasing to note that the adjunctions corresponding to geometric morphisms are those that commute with the double power locale monad; i.e. structure preserving maps. The talk will further explore the many different additional ways that these adjunctions between categories of locales can be characterised. We will prove, in reasonable detail, an omnibus theorem showing that geometric morphisms can also be characterised as:

1.Frobenius adjunctions

2.Stably Frobenius adjunctions

3.Upper and lower power locale monad preserving adjunctions

4.Hilsum-Skandalis maps

5.The connected components adjunction of an internal groupoid

The talk will assume familiarity with topos theory and locale theory.

This talk is part of the Theoretical computer science seminar series.

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