English

Idempotent convexity and algebras for the capacity monad and its submonads

Category Theory 2011-08-08 v2 General Topology

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)(\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)(\max,\min)-idempotent measures) is isomorphic to the category of (max,min)(\max,\min)-idempotent convex compacta and their affine maps.

Keywords

Cite

@article{arxiv.1108.1063,
  title  = {Idempotent convexity and algebras for the capacity monad and its submonads},
  author = {Oleh Nykyforchyn and Dušan Repovš},
  journal= {arXiv preprint arXiv:1108.1063},
  year   = {2011}
}