Geodesic
Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness
Theory and applications of categories, Tome 30 (2015), pp. 909-932.

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We introduce an apparent strengthening of Sufficient Cohesion that we call Stable Connected Codiscreteness (SCC) and show that if $p: E --> S$ is cohesive and satisfies SCC then the internal axiom of choice holds in $S$. Moreover, in this case, $p^!: S --> E$ is equivalent to the inclusion $E_{\neg\neg} --> E$.
Publié le :
Classification : 18B25, 03G30, 18F99
Keywords: Axiomatic cohesion, Topos theory 
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     title = {Internal choice holds in the discrete part
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F. W. Lawvere; M. Menni. Internal choice holds in the discrete part
of any cohesive topos satisfying stable connected codiscreteness. Theory and applications of categories, Tome 30 (2015), pp. 909-932. http://geodesic.mathdoc.fr/item/TAC_2015_30_a25/