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nLab > Latest Changes: homotopy level

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2011
    • (edited Nov 25th 2011)

    created homotopy level

    However, the instiki-table does not come out correctly yet. It did before I added the third column. These tables are the most delicate things. I never know why sometimes they display correctly and sometimes not.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 25th 2011

    The table at the bottom of the entry does not appear as table when seen in my firefox, but as a hard to read list. By the way title in the title of this nForum post.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2011

    title in the title

    I know what you mean ;-) I have fixed it.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 26th 2011

    I just made typo in the typo :)

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeNov 29th 2011

    The table is fixed.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2011
    • (edited Nov 29th 2011)

    Thanks, Toby!

    Can you explain what you did to fix it? Is it that the horizontal line of minus-signs is shorter?

    Do you know what the rules of the game are? Which syntax rule did my original table violate?

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeNov 29th 2011

    First, I copied and pasted the table into a text editor with a larger window size, so that each row would actually fit into one row. Then it became obvious that one of the horizontal lines was supposed to be a vertical line, so I changed it. Then I added a bit to the groupoid column, which ironically made some of the rows even longer, so that they no longer fit into one row even in my larger window!

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2011

    Then it became obvious that one of the horizontal lines was supposed to be a vertical line

    Oh, okay, so I guess I had an evident typo in there. Thanks.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeDec 15th 2011

    I’ve created h-set, h-prop, and equivalence in homotopy type theory, and added corresponding material to contractible type — several definitions in all cases, along with semantic interpretations in model categories. I also moved the theorem “decidable ⇒\Rightarrow set” from set to h-set.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 15th 2011
    • (edited Dec 15th 2011)

    Right now I am having trouble parsing this here, in hSet:

    Paths A+(0→A×A) (Paths A→A×A) ↓ A×A\array{Paths_A + (0\to A\times A)^{(Paths_A\to A\times A)}\\ \downarrow\\ A\times A}

    Is “0” the inital type? What’s the purpose of it here? What is the “+”?

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 15th 2011

    Ah, never mind, I get it from the text below. Maybe I may add some comments on how to read this?

    • CommentRowNumber12.
    • CommentAuthorMike Shulman
    • CommentTimeDec 16th 2011

    Sure.

    • CommentRowNumber13.
    • CommentAuthorTobyBartels
    • CommentTimeDec 18th 2011

    I thought it odd to say that any two elements of an h-set are equal or not when describing an inherently constructive theory. And the point is not that you can say this but that this is all that you can say. So I edited this remark in h-set.

  14. Adding definition, examples, and references

    Anonymous

    diff, v10, current

  15. adding rules for hasHLevel

    Anonymous

    diff, v11, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeDec 28th 2022
    • (edited Dec 29th 2022)

    made a start at adding references:

    These as examples of the actual use of “hlevel”:

    This one for completeness, though it doesn’t say “hlevel”:

    and then the single reference that used to be here (but was just dead link) I have polished up to:

    • Thierry Coquand, Ayberk Tosun, Formal Topology in Univalent Foundations, Ch. 6 in: Proof and Computation II – From Proof Theory and Univalent Mathematics to Program Extraction and Verification, Wold Scientific (2021) [doi:10.1142/12263]

    but I haven’t actually seen this text.

    diff, v12, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2023

    added pointer (here and elsewhere) to:

    diff, v13, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2023
    • (edited Feb 18th 2023)

    added the original reference:

    diff, v14, current

1 to 18 of 18

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