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Perfect toposes and infinitesimal weak generation

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In his 2007 paper on axiomatic cohesion, Bill Lawvere introduced a notion of `weak generation’ of a topos by a family of objects, which has not been much investigated until recently. Last year Matias Menni showed that every sufficiently coherent topos (in Lawvere’s sense) is weakly generated by objects which are `infinitesimal’ in the sense that they are not-not-singletons. We show that weak generation by infinitesimals is equivalent to a much simpler (and older) notion, that of being perfect, which arose out of Peter Freyd’s work on the Cantor coderivative.

This talk is part of the Category Theory Seminar series.

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