State monads and their algebras
Francois Metayer
TL;DR
This paper explores the structure of state monads in cartesian closed categories, demonstrating conditions under which the exponential functor is monadic, thereby advancing understanding of their algebraic properties.
Contribution
It establishes that the exponential functor is monadic in sufficiently regular categories with a non-empty exponent, clarifying the algebraic structure of state monads.
Findings
Exponential functor is monadic under certain regularity conditions.
The structure of algebras for state monads is characterized.
Conditions for monadicity depend on the base category and exponent.
Abstract
State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base category is sufficiently regular, and the exponent is a non-empty object.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Logic, programming, and type systems · Algebraic structures and combinatorial models