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    • CommentRowNumber1.
    • CommentAuthoramyekut
    • CommentTimeNov 25th 2018
    The question is this:

    Suppose C is a category, with a given multiplicatively closed set of morphisms S ⊆ C. The role of the denominator conditions on S is rather similar to the role of a Quillen model structure on C, for which S is the set of weak equivalences. However, the precise relationship between these concepts is not clear to me.

    This question is included in the book
    Derived Categories
    3rd prepubllication version: v3

    In more detail: in Example 6.2.29 in the book I discuss the derived category of commutative DG rings. The main innovation is that there is a congruence on the category of comm DG rings by the quasi-homotopy relation. The passage from the corresponding homotopy category to the derived category is a right Ore localization. (There is a similar story for NC DG rings, but another homotopy is used to formulate quasi-homotopies.) The question above is Remark 6.2.30 there.

    This issue is also touched upon in my paper
    The Squaring Operation for Commutative DG Rings
    and in the lecture notes
    The Derived Category of Sheaves of Commutative DG Rings

    If participants of the forum have some ideas on this matter, I would like to hear them, and maybe also mention them in my book.

    Amnon Yekutieli
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2018

    Welcome Amnon! Thanks for forwarding your question here.