Abstract
A basic notion for monadic convergence structures is that of partially ordered monad Φ = (φ, ≤,η, μ), where (φ, η, μ) is a monad over SET and (φ, ≤) is a functor from SET to the category acSLAT of almost complete semilattices. We introduce the notion of sup-inverse of an acSLAT-morphism and present some of its properties which are important in our theory. After defining the notion of partially ordered monad, there are given some examples, e.g. that of partially ordered fuzzy filter monad and of partially ordered fuzzy stack monad. Because of the generality considered here, microobjects may appear. For each partially ordered monad the notion of stratification is introduced.
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Gähler, W. (2003). Monadic Convergence Structures. In: Rodabaugh, S.E., Klement, E.P. (eds) Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0231-7_3
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DOI: https://doi.org/10.1007/978-94-017-0231-7_3
Publisher Name: Springer, Dordrecht
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