Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness

F. W. Lawvere and M. Menni

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 $E_{\neg\neg} --> E$.

Keywords: Axiomatic cohesion, Topos theory

2010 MSC: 18B25, 03G30, 18F99

Theory and Applications of Categories, Vol. 30, 2015, No. 26, pp 909-932.

Published 2015-06-30.

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