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Categories, Sheaves, and Locales

Seminar by Christian Dahlhausen in autumn term 2018/19.
Tuesday 15-17, Y27 H25

Contents

This seminar provides an introduction to the basic notions of category theory and sheaf theory which both are ubiquitous in pure mathematics and very useful in many contexts. As an application, we will deal in the end with the question whether one could reconstruct a topolological space from only knowing its poset of open subsets. The theory of locales will help us to answer this question.

Literature

Talks

No.DateTitle
017.09.Overview and organisatorial stuff
101.10.Set theory, universes, and categories
208.10.Functors and natural transformations
315.10.Limits and colimits
422.10.Adjoint functors
529.10.Presheaves and sheaves
605.11.Stalks and sheafification
712.11.Sheaves as étalé spaces
819.11.Frames and locales
926.11.Points and sober spaces
1003.12.Spatial locales and sober spaces