arXiv subjects

Tomas Crhak

Publications and source records attributed to Tomas Crhak.

2 recordsLinked to original sources

arXiv2020

On functors from category of Giry algebras to category of convex spaces

In The factorization of the Giry monad (arXiv:1707.00488v2) the author asserts that the category of convex spaces is equivalent to the category of Eilenberg-Moore algebras over the Giry monad. Some of the statements employed in the proof of this claim have been refuted in our earlier paper (arXiv:1803.07956). Building on the results of that paper we prove that no such equivalence exists and a parallel statement is proved for the category of super convex spaces.

math.CT↗

arXiv2018

A note on $σ$-algebras on sets of affine and measurable maps to the unit interval

In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $σ$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the $σ$-algebra induced by the evaluation maps. The author asserts that, under the assumptions given in the paper, the two $σ$-algebras coincide. We give examples contradicting this statement.

math.CT↗