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Graduate Student Homotopy Theory Seminar: An introduction to 2-categories

Event Type
341 Altgeld Hall
Mar 25, 2022   3:00 pm  
Yigal Kamel
Doron Grossman-Naples

This talk will be a survey of some of the basic notions and facts about 2-categories. After introducing 2-categories and various types of functors between them, we will consider constructions that map 2-categories to more familiar objects. On one hand, viewing a 2-category as a “poor” higher category, we can “reduce” it to an ordinary category, via a homotopy construction. On the other hand, viewing a 2-category as a “rich” ordinary category, we can “uplift” it to a simplicial set, via the duskin nerve. I will talk about these and related ideas, indicate some quirks of the theory, and provide examples along the way.

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