  We prove the existence of semiorthogonal decompositions of derived categories
of Quot schemes of zero-dimensional quotients on curves in terms of derived
categories of symmetric products of curves. The above result is a categorical
analogue of a similar formula for the class of Quot schemes in the Grothendieck
ring of varieties by Bagnarol-Fantechi-Perroni. It is a special case of a more
general Quot formula of relative dimension one, which is regarded as a Bosonic
counterpart of the Quot formula conjectured by Jiang and proved by the author.
The proof involves categorical wall-crossing formula for framed one loop
quiver, which itself is motivated and has applications to categorical
wall-crossing formula of Donaldson-Thomas invariants.
