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 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 sheaves 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. Page created, but author did not leave any comments.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeOct 5th 2022

    Tarski universes are supposed to refer to the entire structure consisting of a type UU and the type family ElEl, not just the type UU. So the corresponding name should be “univalent type with a type family” rather than “univalent index type of a type family”.

  2. Renamed due to parallels with other univalent objects like univalent category and univalent universe

    Anonymous

    v1, current

  3. expanded article significantly and renamed article to Tarski universe; the whole reason why one would want such an object is to build up various notions of Tarski universes in type theory, which may or may not be strictly or weakly closed under various type formers in the type theory

    Anonymous

    diff, v6, current

  4. added section on hierarchies of Tarski universes

    Anonymous

    diff, v7, current

  5. added a definition of Tarski universe which does not involve a type family. This parallels the case in set theory where a family of sets is the fibers of a function rather than being a primitive concept.

    Anonymous

    diff, v25, current

  6. added paragraph about definitional univalence for Tarski universes

    Anonymous

    diff, v26, current

  7. added a section regarding closure of universes under all propositions.

    Anonymous

    diff, v30, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2023

    added what I guess is the original reference:

    and expanded out this bibitem:

    The entry used to point the reader to section 2.1.6 in there. But at least the above pdf version has no such section, instead the section titled “Universes” is 2.3.5. So I changed this, but let me know if I am missing something.

    diff, v31, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2023

    added pointer to:

    diff, v32, current