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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 $E_{\neg\neg} --> E$.
@article{TAC_2015_30_a25,
author = {F. W. Lawvere and M. Menni},
title = {Internal choice holds in the discrete part
of any cohesive topos satisfying stable connected codiscreteness},
journal = {Theory and applications of categories},
pages = {909--932},
publisher = {mathdoc},
volume = {30},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a25/}
}
TY - JOUR AU - F. W. Lawvere AU - M. Menni TI - Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness JO - Theory and applications of categories PY - 2015 SP - 909 EP - 932 VL - 30 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2015_30_a25/ LA - en ID - TAC_2015_30_a25 ER -
%0 Journal Article %A F. W. Lawvere %A M. Menni %T Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness %J Theory and applications of categories %D 2015 %P 909-932 %V 30 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2015_30_a25/ %G en %F TAC_2015_30_a25
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/