Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Joost Nuiten
Affiliation:

Utrecht University
Date:

Thu, 2018-03-08 16:30 - 17:30 Classical obstruction theory studies the extensions of a continuous map along a relative CW-complex in terms of cohomology with local coefficients. In this talk, I will describe a similar obstruction theory for $(\infty, 1)$- and $(\infty, 2)$-categories, using cohomology with coefficients in local systems over the twisted arrow category and the `twisted 2-cell category'. As an application, I will give an obstruction-theoretic argument that shows that adjunctions can be made homotopy coherent (as proven by Riehlâ€“Verity). This is joint work with Yonatan Harpaz and Matan Prasma.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/7958