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Alex Simpson: 'Three toposes for probability and randomness'
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Topos Institute Colloquium, 6th of June 2024.
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I shall give a brief guided tour of three toposes that have arisen in a research programme to model aspects of probability and randomness from a topos perspective. The first topos of "probability sheaves" supports a synthetic style of probabilistic reasoning about random variables. The second "random topos" makes sense of the notion of "random element" and models a world in which all sets are measurable. The third topos of "random probability sheaves" combines the previous two and provides a home for a more radical style of "synthetic probability theory" expunged of all concerns about sigma-algebras, measurability and the like.
———
I shall give a brief guided tour of three toposes that have arisen in a research programme to model aspects of probability and randomness from a topos perspective. The first topos of "probability sheaves" supports a synthetic style of probabilistic reasoning about random variables. The second "random topos" makes sense of the notion of "random element" and models a world in which all sets are measurable. The third topos of "random probability sheaves" combines the previous two and provides a home for a more radical style of "synthetic probability theory" expunged of all concerns about sigma-algebras, measurability and the like.
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