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nLab > Latest Changes: coequalizer type

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  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

    and

    ∏c:A×Aπ1(c)=Aπ2(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=1 (which is a set) then the coequalizer of the two projections is the circle S1, which is not the propositional truncation of 1.

    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

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