Mathematics Wiskunde

Tuesday 6 February 2024

Exploring some categorical aspects of foundational concepts in algebraic geometry.

Speaker: Damas Mgani
Time: 13:00
Venue: Mathematics Division, Room 1006

After presenting the outline of the entire thesis, we will shift our focus to a categorical perspective on gluing. We will guide you through the process of extracting the gluing index category and the concept of a gluing data functor from the conventional gluing topological data. Additionally, we will introduce the notion of a refinement morphism for gluing data functors, allowing us to combine and “compose” these functors. Through a concrete example, we will illustrate how these gluing processes can be applied. We will then discuss all the categories in which we have demonstrated the existence of glued-up objects. Finally, we will conclude the talk by demonstrating how gluing data functors define coverings that establish a Grothendieck topology on the category of topological spaces.

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