On lax-algebraic (co)nuclei

Abstract

Quantic (co)nuclei provide a convenient technique for constructing quotients and subquantales of quantales. This paper shows its analogue for the laxalgebraic approach to topology of M. M. Clementino, D. Hofmann, and W. Tholen, based in a monad and a unital quantale. As a result, we get a machinery for constructing quotient categories and subcategories, which provides, in particular, several of the already de ned ones by M. M. Clementino et al. We also get a representation theorem for the approach of M. M. Clementino et al.