Geodesic
Filter Monads, Continuous Lattices and Closure Systems
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 50-59

Voir la notice de l'article provenant de la source Cambridge University Press

The notion of a monad (triple) has become increasingly important as an extension of the classical universal algebraic approach to “algebraic” categories. Indeed the categories of algebras arising from a monad seem to be the most natural generalization of Birkhoffs equational classes. Moreover in [2], Barr's concept of a relational model of a monad also coincides nicely with both the concepts of partial algebras (when suitably restricted) and (Moore) closure systems.In this paper, we wish to examine two particular monads determined by filters. The first is the filter monad F = (F, η, μ) over Sets where FX is the set of all (not necessarily proper) filters on X. 
Day, Alan. Filter Monads, Continuous Lattices and Closure Systems. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 50-59. doi: 10.4153/CJM-1975-008-8
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