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1. • CommentRowNumber1.
   • CommentAuthorKeithEPeterson
   • CommentTimeDec 20th 2016
   • (edited Dec 20th 2016)
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   Author: KeithEPeterson
   Format: MarkdownItexIs the [core](https://ncatlab.org/nlab/show/core) of a category always a [wide subcategory](https://ncatlab.org/nlab/show/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](https://ncatlab.org/nlab/show/calculus+of+fractions).

   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.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeDec 20th 2016
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   Author: Mike Shulman
   Format: MarkdownItexCertainly it is.

   Certainly it is.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeDec 21st 2016
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   Author: TobyBartels
   Format: MarkdownItexIf your edited question is this: Let $C$ be a category and let $W$ be the class of isomorphisms of $C$; note that $W$ is closed under composition and so defines a subcategory of $C$, which is the core of $C$. Must $(C,W)$ 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.)

   If your edited question is this:

   Let $C$ be a category and let $W$ be the class of isomorphisms of $C$; note that $W$ is closed under composition and so defines a subcategory of $C$, which is the core of $C$. Must $(C,W)$ 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.)