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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\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

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