nLab
monadic algebra

Monadic algebras

Idea

Monadic algebras are type one modal algebras, in which the single operator behaves like a closure operation in a topological space, (so these are closure algebras) and, in addition, elements are closed if and only if they are open.

Definitions

Definition

A monadic algebra is a closure algebra, (𝔹,m)(\mathbb{B}, m), which satisfies: for all xx, xlmxx\leq l m x, where, as usual, ll is a shorthand for ¬m¬\neg m \neg.

Revised on December 24, 2010 07:18:48 by Toby Bartels (75.88.75.53)