Strongly self-absorbing $C^*$-algebras and Fra\"iss\'e limits

Abstract

We show that the Fra\"iss\'e limit of a category of unital separable $C^*$-algebras which is sufficiently closed under tensor products of its objects and morphisms is strongly self-absorbing, given that it has approximate inner half-flip. We use this connection between Fra\"iss\'e limits and strongly self-absorbing $C^*$-algebras to give a self-contained and rather elementary proof for the well known fact that the Jiang-Su algebra is strongly self-absorbing.