Inner products of 2-representations

We define and calculate inner products of 2-representations. Along the way, we prove that the categorical trace Tr(−) of [24, Sec. 3] is multiplicative with respect to various notions of categorical tensor product, and we identify the center of the category of equivariant objects. We discuss applications, ranging from Schur's result about the number of irreducible projective representations to a formula for the Hochschild cohomology of a global quotient orbifold.