2-Bayesian Update as Homotopy Pushout in the Derived Category of 𝐷 𝑋

Abstract

We study the update of Bayesian update maps (2-Bayesian update) by formulating update maps as morphisms in the derived category Db(DX). We show that deformations of update maps are classified by Ext1 and that the universal synthesis of multiple update maps is given by the homotopy pushout. An explicit construction is obtained as the shifted mapping cone Cone(f−g)[−1].