Mardare, Panangaden and Plotkin introduced C-varieties of algbebras on metric spaces. These are categories of metric-enriched algebras specified by equations in a context. A context puts restrictions on the distances of variables one uses. We prove that C-varieties are precisely the monadic categories over Met for countably accessible enriched monads preserving epimorphisms.
We analogously introduce C-varieties of ordered algebras as categories specified by inequalities in a context. Which means that conditions on inequalities between variables are imposed. We prove that C-varieties precisely correspond to enriched finitary monads on Pos preserving epimorphisms.
This is joint work with Jiří Rosický. This is based on this arXiv paper.
This video is part of Masaryk University‘s Algebra seminar.
