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    • CommentRowNumber1.
    • CommentAuthorKeithEPeterson
    • CommentTimeDec 20th 2016
    • (edited Dec 20th 2016)

    Is the core of a category always a wide subcategory? I mean, in the most laziest sense of isomorphisms, why not include identity morphisms?

    Edit: I’m curious if cores always have a notion of fraction.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 20th 2016

    Certainly it is.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeDec 21st 2016

    If your edited question is this:

    Let CC be a category and let WW be the class of isomorphisms of CC; note that WW is closed under composition and so defines a subcategory of CC, which is the core of CC. Must (C,W)(C,W) admit a calculus of right fractions?

    then the answer is yes. (And the situation is symmetric, so it also admits a calculus of left fractions.)

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