Generating the algebraic theory of C(X): the case of partially ordered compact spaces [article]

Dirk Hofmann, Renato Neves, Pedro Nora
2017 arXiv   pre-print
It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by _1. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is a _1-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms. We also characterise the _1-copresentable partially ordered compact spaces.
arXiv:1706.05292v1 fatcat:kddwo2kejnfxzbk6am76ms5ovi