Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 25th 2024

    For now creating page, it needs to be (much) further expanded.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 25th 2024
    • (edited Jan 25th 2024)

    Thanks for your recent edits, and in particular for looking into starting a page of this kind here, which has long been missing.

    \,

    Just for the record I’ll voice my usual complaint about terminology:

    The word “categorical” means: without exceptions or conditions; absolute; unqualified; unconditional.

    This is of course not what is meant here.

    \,

    In the present context the correct adjective is instead: “category-theoretic”.

    A better title for this entry would be, in my opinion: category theoretic probability.

    Now, I am aware that I am far outnumbered in holding this opinion.

    Still, I feel that saying “categorical” for “category theoretic” is just wrong.

    Just saying. Don’t let that stop you. Feel free to ignore me on this point.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 25th 2024

    If it’s of any use to you, Paolo, I have dumped a load of references here which at least are in nLab format.

    • CommentRowNumber4.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 25th 2024

    Thank you, that’s very helpful!

    • CommentRowNumber5.
    • CommentAuthorHurkyl
    • CommentTimeJan 25th 2024

    Wasn’t there a convention to use “categorial” as the adjective for things related to category theory?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2024
    • (edited Jan 26th 2024)

    use “categorial” as the adjective for things related to category theory?

    In ordinary English language there seems to be no real difference in meaning between “categorical” and “categorial”; cf. e.g. English.StackExchange/a/519672 (?)

    (Also in German, for example, there are not even two such distinct words available, there is only kategorisch.)

    But since “categorial” seems not to be used much in common speaking, it might at least be a better choice than “categorical” if one insists on abusing common terminology in the first place.

    \,

    (For what purpose, though? “category-theoretic” is precise, pronounced, and shorter than “categori(c)al approach”. Categories in themselves are not noteworthy; it is the theory of categories that usefully informs other fields like, in the present case, probability theory. If terminology can reflect that, it should.)

    • CommentRowNumber7.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 26th 2024
    • (edited Jan 26th 2024)

    Changed the title to “category-theoretic”. All of you are making good points, and there’s also the additional point that “categorical random variables” in probability means “with values in a discrete set rather than real numbers”. And I want to avoid all possible confusion, we do consider real numbers here.

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2024

    All right, thanks!

    May I still lobby for shortening it to category-theoretic probability? :-)

    • CommentRowNumber9.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 30th 2024

    Added more detailed list of existing results. (Still widely incomplete, especially on the quantum and CS side.)

    diff, v14, current

  1. Added tags

    Fabio Zanasi

    diff, v30, current

  2. Added tags

    Fabio Zanasi

    diff, v30, current