Seminar: Parametrized semiadditivity

Content

We will give an introduction to the theory of parametrized semiadditivity, following the treatment of [CLL24]. The precise content is still to be established, but will at least entail:

• A discussion of parametrized (higher) category theory and the corresponding notion of parametrized colimits;

• The definition of parametrized semiadditivity, characterizations and examples;

• The definition of the parametrized span category and a proof of its universal property;

• The characterization of parametrized semiadditivity via a tensoring by the span category;

• The definition of parametrized commutative monoids and their universal properties;

• The relation with Mackey sheaves / sheaves with transfers;

• A discussion of equivariant semiadditivity;

• A discussion of higher semiadditivity in chromatic homotopy theory;

• A discussion of parametrized semiadditivity in the Kasparov K-theory categories.

Date, time, location

The seminar takes place weekly on Tuesday from 16:15 - 17:45 in M101.