Uncertainty in category theory

General

• Johnson & Rosebrugh, 2003: Three approaches to partiality in the sketch data model (doi, pdf)
• Marsden, 2016: Ambiguity and incomplete information in categorical models of language (arxiv, pdf, slides)
  • General strategy:
    1. Define a commutative monad $T$ on $\mathbf{Set}$
    2. Its Eilenberg-Moore algebras form a bicomplete, closed symmetric monoidal category $\mathrm{EM}(T)$
    3. Take categories enriched in $\mathrm{EM}(T)$, usually generated freely from an existing category like $\mathbf{Rel}$ or $\mathbf{FdHilb}$
  • Includes both qualitative and quantitative models
  • The qualitative models are not very convincing

Probabilistic

TODO