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arXiv · 1108.1063

Idempotent convexity and algebras for the capacity monad and its submonads

Oleh Nykyforchyn·Dušan Repovš
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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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Oleh Nykyforchyn, Dušan Repovš. 2011-08-05. Idempotent convexity and algebras for the capacity monad and its submonads. https://doi.org/10.1007/s10485-010-9229-9

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