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).

nLab > Latest Changes: unit type

Bottom of Page

1 to 8 of 8

  1.  

  1. clarifying the categorical semantics section

    Anonymous

    diff, v13, current

  2. adding section about positive and negative unit types in dependent type theory with typal computation and uniqueness rules, formalised in natural deduction

    Anonymous

    diff, v14, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2022
    • (edited Dec 17th 2022)

    I have hyperlinked more of the technical terms.

    Also touched the wording in some places, for streamlining.

    diff, v16, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2023
    • (edited Jan 3rd 2023)
    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeMar 27th 2023

    added a section about the unit type as a univalent universe

    diff, v20, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2023

    Dear Anonymous Guest,

    The first sentence in your edit is

    The unit type could also be represented as a univalent universe.

    Instead of “could” you mean “can” or “may”. Instead of “represented” you mean “regarded”.

    The last sentence of your addition is:

    The extensionality principle for the unit type then is simply the univalence axiom:

    It hardly “is the univalence axiom”. Rather, it’s a completely degenerate variant oft it.

    Even if we were to fix these sentences, I have trouble seeing what is useful about your paragraph.

    Why are you adding such material, what motivates you? And why are you still hiding in anonymity?

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMar 27th 2023

    added a paragraph explaining why it is useful to consider the unit type as a universe: universes in type theory correspond to regular and inaccessible cardinals in set theory

    also added a sentence explaining that yes indeed the unit type represents a trivial universe where every type is contractible.

    diff, v21, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2023

    Thanks for reacting, I appreciate it. That looks better.

1 to 8 of 8

  1.