3 citations · 4 across the 5 of their papers we have counts for
6 papers
Varieties of Quantitative or Continuous Algebras (Extended Abstract)
Jiří Adámek, Matěj Dostál, Jiří Velebil
Quantitative algebras are algebras enriched in the category of metric spaces so that all operations are nonexpanding. Mardare, Plotkin and Panangaden introduced vari…
Sifted Colimits, Strongly Finitary Monads and Continuous Algebras
Jiří Adámek, Matěj Dostál, Jiří Velebil
We characterize strongly finitary monads on categories , and as precisely those preserving sifted colimits. Or, equivalently, enriched…
Quantitative Algebras and a Classification of Metric Monads
J. Adámek, M. Dostál, J. Velebil
Quantitative algebras are -algebras acting on metric spaces, where operations are nonexpanding. Mardare, Panangaden and Plotkin introduced 1-basic varieties as categories of qua…
A categorical view of varieties of ordered algebras
J. Adámek, M. Dostál, J. Velebil
It is well known that classical varieties of -algebras correspond bijectively to finitary monads on . We present an analogous result for varieties of ordered -a…
Bénabou's theorem for pseudoadjunctions
Matěj Dostál
We give a formal account of Bénabou's theorem for peudoadjunctions in the context of Gray-categories. We prove that to give a pseudoadjunction with unit i…
A two-dimensional Birkhoff's theorem
Matěj Dostál
Birkhoff's variety theorem from universal algebra characterises equational subcategories of varieties. We give an analogue of Birkhoff's theorem in the setting of enrichment in cat…