#
Cohesive toposes of sheaves on monoids of continuous endofunctions of the unit interval

##
Luis Jesús Turcio

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.

http://www.tac.mta.ca/tac/volumes/35/29/35-29.pdf

Revised 2020-08-05. Original version at

http://www.tac.mta.ca/tac/volumes/35/29/35-29a.pdf

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