Towards functor exponentiation

Abstract

We consider a possible framework to categorify the exponential map exp(-f) given the categorification of a generator f of ${\mathfrak{sl}}_2$ by Lauda. In this setup the Taylor expansions of exp(-f) and exp(f) turn into complexes built out of categorified divided powers of f. Hom spaces between tensor powers of categorified f are given by diagrammatics combining nilHecke algebra relations with those for a additional "short strand" generator. The proposed framework is only an approximation to categorification of exponentiation, because the functors categorifying exp(f) and exp(-f) are not invertible.

27 pages

References in corpus (4)

• 2-Kac-Moody algebras
• FI-modules and stability for representations of symmetric groups
• How to categorify the ring of integers localized at two
• Towards a categorical boson-fermion correspondence