  We relate the Algebra of the Infrared of Gaiotto-Moore-Witten with the theory
of perverse schobers which are (conjectural, in general) categorical analogs of
perverse sheaves. A perverse schober on a complex plane C can be seen as an
algebraic structure that can encode various categories of D-branes of a
2-dimensional supersymmetric field theory, as well as the interaction
(tunnelling) between such categories. We show that many constructions of the
Algebra of the Infrared can be developed once we have a schober on C. These
constructions can be seen as giving various features of the analog, for
schobers, of the geometric Fourier transform well known for D-modules and
perverse sheaves.
