Zigzags and free adjunctions

Abstract: The cobordism hypothesis tells us that the process of freely adding adjoints to the $k$-morphisms of a symmetric monoidal $(\infty,n)$-category can be roughly described as follows: treat one such $k$-morphism as an $n$-framed $k$-dimensional cube and change the framing appropriately to obtain its left/right adjoint. At the very least, this description is correct if we start with the the commutative monoid generated by a single object. But what happens with more complicated examples? Motivated by work of Dawson-Paré-Pronk, we explicitly construct the functor that freely adds right adjoints to the morphisms of an infinity-category; we also extend the construction to arbitrary dimensions and speculate on what its universal property should be. This is based on joint work with Martina Rovelli.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)