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nLab > Latest Changes: Model Categories and More General Abstract Homotopy Theory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 24th 2022

    Created:

    A historically important early manuscript draft.

    This manuscript draft later transformed in Homotopy Limit Functors on Model Categories and Homotopical Categories, adding Jeffrey H. Smith as a coauthor.

    However, the draft serves as an original reference for the Kan recognition theorem (in §II.8) and the Kan transfer theorem (in §II.9), as well as cofibrantly generated model categories (in Chapter II).

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 24th 2022

    Added:

    Furthermore, this draft originates the modern definition of a model category (in §I.1.2), modifying the original definition of closed model category by Quillen by replacing finite (co)limits with small (co)limits and requiring factorizations to be functorial.

    All this material did not make it to the book.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 24th 2022

    Added:

    The first mention of monoidal model categories (without the unit axiom) under this name is in Remark 55.10, with no definition given, but the preceding section discusses the pushout product axiom.

    v1, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 8th 2022

    touched formatting of the reference and added mentioning of Reedy model structures

    diff, v4, current

1 to 4 of 4

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