English

Sifted Colimits, Strongly Finitary Monads and Continuous Algebras

Category Theory 2023-10-12 v2

Abstract

We characterize strongly finitary monads on categories Pos\mathsf{Pos}, CPO\mathsf{CPO} and DCPO\mathsf{DCPO} as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study sifted colimits in general enriched categories. For CPO\mathsf{CPO} and DCPO\mathsf{DCPO} we characterize varieties of continuous algebras as precisely the monadic categories for strongly finitary monads.

Keywords

Cite

@article{arxiv.2301.05730,
  title  = {Sifted Colimits, Strongly Finitary Monads and Continuous Algebras},
  author = {Jiří Adámek and Matěj Dostál and Jiří Velebil},
  journal= {arXiv preprint arXiv:2301.05730},
  year   = {2023}
}