We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere's category and we show convexity, lower semicontinuity and uniqueness.

@article{paperbot2184,
  title = {A categorical characterization of relative entropy on standard Borel spaces},
  author = {Nicolas Gagne and Prakash Panangaden},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 19, Issue 4},
  year = {2023},
  doi = {10.46298/lmcs-19(4:10)2023}
}