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 comma 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 finite 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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).
  1. starting article on class theory

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2022
    • (edited Nov 19th 2022)

    Thanks for these substantial additions.

    Just some trivia on formatting and style:

    • To set the scene for the reader, I have prefixed the opening sentence by the words “In the foundations of mathematics…” (also included the respective floating context menu).

    • Where “material and structural” are first mentioned, I have hyperlinked these words.

    • The two long sentences that followed I have taken the liberty of breaking up for readability: I have turned “… and classes are…” into “… Here, classes are…”

    • Generally, I have hyperlinked more of the technical terms, such as theory, formulae, size issue, model, higher structure etc.

    • Speaking of higher structures: it remains unclear to me what the following paragraph currently in the entry is meant to achieve:

    While class theories address the issue of size in mathematics, they violate the principle of equivalence for higher structures like groupoids, because, like sets in set theory, every class in class theory has propositional equality, including groupoids defined in class theory.

    It seems to me the two issues here are orthogonal to each other. Or maybe you are thinking specifically of large groupoids, like the groupoid of all sets? If so, that would be good to clarify.

    diff, v3, current

  2. Adding reference

    • Henrik Forssell, Categorical Models of Intuitionistic Theories of Sets and Classes. Master’s thesis, Carnegie Mellon University, 2004. (PDF)

    Anonymous

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2022

    Let me know if you have thoughts regarding the last point in #2. Otherwise I feel like deleting the paragraph in question there, since in its current form it does not seem to make sense.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 22nd 2022

    In lack of a reply to my question in #2, I am removing this paragraph from the entry:

    While class theories address the issue of size in mathematics, they violate the principle of equivalence for higher structures like groupoids, because, like sets in set theory, every class in class theory has propositional equality, including groupoids defined in class theory.

    I don’t see how this makes sense as formulated. If anyone sees what was meant and can expand, please do and we put the paragraph back in.

    diff, v7, current