As recently illustrated by Ludewig and Roos, second quantization of fermions, i.e., the algebraic construction associating with a quadratic vector space its Clifford algebra and with a Lagrangian relation its exterior algebra (the Fock module) is an anomalous functor with values in the Morita 2-category of (super)algebras, bimodules and bimodule morphisms, with anomaly given by determinant lines. This can be equivalently seen as a projective 2-representation of the category of Lagrangian relations. The commutativity of diagrams expressing the relevant coherence conditions can be checked  by a direct computation using specific properties of the Clifford/Fock construction. Yet, this approach would hide the true nature of the proof, that works universally and only uses the invertibility of Clifford algebras and of Fock bimodules in the Morita 2-category of (super)algebras. We will present a proof of the universal construction using the language of invertible 2d TQFTs with invertible defects. Based on joint work in progress with Chetan Vuppulury.