Probabilistic and Namespace Conditioning in Poly

Abstract

In the category of Polynomial functors, the substitution monoidal product \mathbin{\triangleleft} is not symmetric. In this talk, we will explore how distributive maps p \mathbin{\triangleleft} q \to q \mathbin{\triangleleft} p give notions of “conditioning”. These notions in probabilistic conditions (such as “conditioned on it being sunny, what is the probability that I will go outside”) and namespace conditioning (such as searching “what directories satisfy the condition of containing 3 files”). Of particular interest will be a derivation of Bayesian inference, whose key insight is a simple braiding map.