On dependent type theory and its categorical semantics (categorical semantics of dependent types):
Bart Jacobs, Comprehension categories and the semantics of type dependency, Theoret. Comput. Sci. 107 2 (1993) 169-207 [MR1201808, doi:10.1016/0304-3975(93)90169-T]
Bart Jacobs, Categorical Logic and Type Theory, Studies in Logic and the Foundations of Mathematics 141, Elsevier (1998) [ISBN:978-0-444-50170-7, pdf, webpage]
On category theoretic probability theory (cf. convex powerset of distributions monad):
Bart Jacobs, Coalgebraic trace semantics for combined possibilitistic and probabilistic systems, Proceedings of CMCS 2008, ENTCS 203 5 (2008) 131-152 [doi:10.1016/j.entcs.2008.05.023]
Bart Jacobs, Structured Probabilistic Reasoning, (pdf)
On CD-categories (gs-monoidal categories) and what came to be known as Markov categories (affine CD categories):
On bases for algebras of an endofunctor in terms of coalgebras:
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