Geodesic
Cohesive toposes of sheaves on monoids of continuous endofunctions of the unit interval
Theory and applications of categories, Tome 35 (2020), pp. 1087-1100

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18F60, 18F10
Keywords: TAC, Cohesion, Topos theory 
@article{TAC_2020_35_a28,
     author = {Luis Jes\'us Turcio},
     title = {Cohesive toposes of sheaves on monoids of continuous endofunctions of the unit interval},
     journal = {Theory and applications of categories},
     pages = {1087--1100},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a28/}
}
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Luis Jesús Turcio. Cohesive toposes of sheaves on monoids of continuous endofunctions of the unit interval. Theory and applications of categories, Tome 35 (2020), pp. 1087-1100. http://geodesic.mathdoc.fr/item/TAC_2020_35_a28/