1975/02/01 by Alan Day · 9 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Algebraic number #Closure (psychology) #Computer science #Discrete mathematics #Extension (predicate logic) #Filter (signal processing) #Functor #Generalization #Homotopy and Cohomology in Algebraic Topology #Logic, Reasoning, and Knowledge #Mathematical analysis #Mathematics #Monad (category theory) #Programming language #Pure mathematics #Set (abstract data type)
paper · pdf · doi:10.4153/cjm-1975-008-8
openalex publication_date 1975/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.