On Eilenberg-Moore algebras induced by chains
Copyright policy )On Eilenberg-Moore algebras induced by chains
Given a fixed topological space, consider the monad \(\mathbb{T}_S\) on \({\mathcal S}et\) determined by the contravariant \(\text{hom}\) functor of \(S\) and its adjoint \((-)^S\). The Eilenberg-Moore category of \(\mathbb{T}_S\) has been determined by Linton for the Sierpiński dyad and by \textit{R.-E. Hoffmann} for all spaces of cardinality \(\leq 2\) [Seminarberichte FernUniversität Hagen 19, 207-216 (1984)]. The present paper characterizes the Eilenberg-Moore algebras of \(\mathbb{T}_S\) for finite chains \(S\) with their upper topology in terms of frames and actions.
- University of South Africa South Africa
Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, Heyting algebras (lattice-theoretic aspects), Algebraic structures, Eilenberg-Moore and Kleisli constructions for monads, complete dual frame, Eilenberg-Moore algebra, Categorical methods in general topology, C(S)-action, Frames, locales, Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, Heyting algebras (lattice-theoretic aspects), Algebraic structures, Eilenberg-Moore and Kleisli constructions for monads, complete dual frame, Eilenberg-Moore algebra, Categorical methods in general topology, C(S)-action, Frames, locales, Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
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