Idempotent Convexity and Algebras for the Capacity Monad and its Submonads |
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| Authors: | Oleh Nykyforchyn Dušan Repovš |
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| Affiliation: | 1.Department of Mathematics and Computer Science,Vasyl’ Stefanyk Precarpathian National University,Ivano-Frankivsk,Ukraine;2.Faculty of Mathematics and Physics, and Faculty of Education,University of Ljubljana,Ljubljana,Slovenia |
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| Abstract: | Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of (max, min)-idempotent biconvex compacta and their biaffine maps. It is also shown that the category of algebras for the monad of sup-measures ((max, min)-idempotent measures) is isomorphic to the category of (max, min)-idempotent convex compacta and their affine maps. |
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