Monoidal structure of the Khovanov homotopy type

Recently, Lawson, Lipshitz and Sharkar proved that the Khovanov
homotopy type, that assigns to any link diagram certain object in the
Spanier-Whitehead category, is functorial, i.e., maps induced by link
cobordisms are invariant under isotopies. Similar results holds for pointed
links.

Both the category of links and the Spanier-Whithead category can be equipped
with very natural symmetric monoidal structures. As it turns out, the
Khovanov homotopy type functor becomes a symmetric monoidal functor.
The goal of the talk will be to describe monoidal structures on the
categories of links and pointed links and discuss the proof of monoidality
of the Khovanov homotopy type functor.

The talk is based on the paper of Lawson, Lipshitz, Sharkar, "Khovanov
homotopy type, Burnside category, and products”.