Eigil Rischel

@AyeGill

Master's Student. Category theory.

Vrijeme pridruživanja: studeni 2012.

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  1. 17. sij

    Given a conditional distribution X -> PY (map from X to distributions on Y), and y \in Y, the resulting "Bayesian update" PX -> PX is not a Kleisli map - it does not preserve convex combinations/mixtures of distributions. How should I think about this? Where does this map live?

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  2. 16. sij

    Arguably most of the really great historical successes in pure math have to do with A, while B is much bigger in applied category theory (where e.g. ZX calculus, one of the big success stories, seems mostly to be about this)

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  3. 16. sij

    Discussion about the utility of applied category theory made me realzie there are really two distinct "dimensions" of cat. th: A) Describing things by their transformations. (Universal properties) B) Describing things by building them out of simpler things ("Compositionality").

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  4. 15. sij

    It may just be functions A × B → [0,\infty), but I'm hoping there's a way of doing this that makes it easier to compare to the regular categories version

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  5. 15. sij
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  6. 15. sij

    Fill this table (A, B are sets/metric spaces/topological spaces/whatever): Function A → B : Relation between A and B : Function A ← B Stochastic process A → B : ???? : Stochastic process A ← B. Looking for a graphical probabilistic logic similar to the one for relations.

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  7. 4. sij

    My motivation is coming from metric spaces - I want transitivity of equality to correspond to the triangle inequality. But subterminal objects in cat. of metric spaces are just (Ø, 1), so I guess to model this logic fully you need to combine with some sort of fuzzy set.

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  8. 4. sij

    Trying to find a good [0,∞]-valued logic (where the implication is >, so 0 is truth), where + is used as conjunction (rather than max). Also looking for good notion of categorical model - topoi can't do this, their logic is contractive (i.e a => a & a, but a < a + a).

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  9. 6. pro 2019.

    Shoutout to for example 3.8

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  10. 6. pro 2019.

    I've written a paper on describing probability theory using category theory, with Tobias Fritz. It can now be found on arXiv:

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  11. 9. stu 2019.

    What are the properties/structure/data of a morphism A -> B that makes it an "approximation"? Ie i would say that the floor map R -> Z "is an approximation", but not the map sin : R -> [0,1].

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