Idempotent convexity and algebras for the capacity monad and its submonads

Details Idempotent convexity and algebras for the capacity monad and its submonads Idempotent convexity and algebras for the capacity monad and its submonads

2011-08-04

arxiv.org/abs/1108.1063v2

Applied Categorical Structures 19:4 (2011), 709-727

Mathematics

Category Theory

Scientific paper

10.1007/s10485-010-9229-9

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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