University of Cambridge > Talks.cam > Category Theory Seminar > Trees for subtoposes of the effective topos

Trees for subtoposes of the effective topos

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For making concrete calculations about subtoposes of the effective topos, it is crucial to have a tangible representation of the corresponding local operators. We introduce tree-like structures called `sights’, in order to further understand a representation due to A.M. Pitts (which arises from the topos-theoretic construction of the least local operator making a given subobject of a topos dense) and to define another useful representation. We apply these methods to establish some new examples of subtoposes, and to compare them to known ones. We also remark that a realizability-like semantics can be formulated for the arithmetic of subtoposes in terms of sights.

This talk is part of the Category Theory Seminar series.

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