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 definitions 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 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 nonassociative 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: coequalizer type

Bottom of Page

1 to 9 of 9

  1.  

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

    Anonymous

    v1, current

  2. The example given (propositional truncation) is only correct up to set truncation.

  3. changed ’type’ to ’h-set’ in example

    Anonymous

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeOct 15th 2022

    @2

    Why does the example of propositional truncation fail for types which aren’t sets?

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeOct 15th 2022

    i.e. what is the difference between

    ∏ a:A∏ b:Aa= Ab\prod_{a:A} \prod_{b:A} a =_A b

    and

    ∏ c:A×Aπ 1(c)= Aπ 2(c)\prod_{c:A \times A} \pi_1(c) =_A \pi_2(c)
    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeOct 16th 2022

    It’s not just that the type has to be a set, but that you have to set-truncate the coequalizer to get the propositional truncation. For instance, if A=1A=1 (which is a set) then the coequalizer of the two projections is the circle S 1S^1, which is not the propositional truncation of 11.

    diff, v3, current

  7. Adding the circle type as an example of a coequalizer

    Anonymous

    diff, v4, current

  8. There was a section about W-suspensions titled “Higher inductive types generated by graphs” in the article coequalizer type, so I moved the section into its own page at W-suspension.

    diff, v7, current

  9. The W-suspensions mentioned in this article are graph quotients. Let us leave the term W-suspension for the HIT defined in the Sojakova article.

    diff, v8, current

1 to 9 of 9

  1.