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nLab > Latest Changes: E-category

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  1. split off from precategory into its own article

    Anonymous

    v1, current

  2. strongly extensional -> which preserves the equivalence relation; strongly extensional is about preserving apartness relations not equivalence relations.

    Anonymous

    v1, current

  3. Renamed all instances of “proset” to “preorder” since there are no set-truncations in the definition, and removed incorrect statement about symmetric preorders being the same as sets in univalent type theory

    Anonymous

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeSep 26th 2022

    Corrected the name to the standard type-theoretic one “E-category”. Similarly, replaced “symmetric preorder” with setoid.

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeSep 26th 2022

    Reading some of the other discussion, it’s possible that I misinterpreted what was meant here. Did you mean to be talking about categories enriched over prop-valued equivalence relations, rather than over setoids?

    It seems clear that there are endless variations on these structures, but it’s not clear to me that we need pages about all of them. I think it’s sensible to have a page about E-categories because they are a standard concept in type theory, but I don’t know that we need a page about equivalence-relation-enriched categories. Is there some intended application?

    Also, please sign your edits with a distinguishable pseudonym!

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