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How to enhance categories, and why

Introductory Workshop: Noncommutative Algebraic Geometry February 05, 2024 - February 09, 2024

February 06, 2024 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Dmitry Kaledin (HSE University; V. A. Steklov Institute of Mathematics)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

How to enhance categories, and why


It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement".  Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view.  I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator".

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How to enhance categories, and why

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