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nLab > Latest Changes: algebraically compact category

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1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorSam Staton
    • CommentTimeJul 16th 2020

    page about algebraic compactness.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2020

    have given some more terms hyperlinks, and added hyperlinked doi-s to the references

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeJul 17th 2020

    include mixed variance

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorSam Staton
    • CommentTimeJul 17th 2020

    coinduction

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorSam Staton
    • CommentTimeJul 18th 2020

    minor correction and mentioning retracts of solutions

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorSam Staton
    • CommentTimeJul 18th 2020

    mention example of pointed cpo’s

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorSam Staton
    • CommentTimeJul 18th 2020

    proof sketch that cpo’s and strict maps are algebraically compact

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 23rd 2020

    As written, the Idea section doesn’t seem to have much content that is specific to algebraic compactness, just very general remarks about data structures being fixed points.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2020
    • (edited Dec 23rd 2020)

    As a minimum fix I have added the following lead-in to the Idea section (hoping that it will prompt some expert to expand/improve on it):

    A category is called algebraically compact if for every endofunctor on it the respective initial algebra coincides with the final coalgebra.

    Under categorical semantics of programming languages this condition ensures the existence of inductive-recursive types (e.g. Zamdzhiev 20). For that, recall:

    …

    diff, v7, current

1 to 9 of 9

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