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We generalise an existing construction of Bayesian Lenses to admit lensesbetween pairs of objects where the backwards object is dependent on states onthe forwards object (interpreted as probability distributions). This gives anatural setting for studying stochastic maps with Bayesian inverses restrictedto the points supported by a given prior. In order to state this formally wedevelop a proposed definition by Fritz of a support object in a Markov categoryand show that these give rise to a section into the category of dependentBayesian lenses encoding a more canonical notion of Bayesian inversion.

Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion