We determine the largest submonoid of the monoid of continuous endomorphisms of the unit interval [0,1] on which the finite partitions form the basis of a Grothendieck topology, and thus determine a cohesive topos over sets. We analyze some of the sheaf theoretic aspects of this topos. Furthermore, we adapt the constructions of Menni to include another model of axiomatic cohesion. We conclude the paper with a proof of the fact that a sufficiently cohesive topos of presheaves does not satisfy the continuity axiom.
Keywords: TAC, Cohesion, Topos theory
2020 MSC: 18F60, 18F10
Theory and Applications of Categories, Vol. 35, 2020, No. 29, pp 1087-1100.
Revised 2020-08-05. Original version at