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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 23rd 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded at _[[core]]_ the remark that the core is right adjoint to the forgetful functor $Grpd \to Cat$.

   added at core the remark that the core is right adjoint to the forgetful functor $Grpd \to Cat$.

2. • CommentRowNumber2.
   • CommentAuthorYuxi Liu
   • CommentTimeJul 2nd 2020
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   Author: Yuxi Liu
   Format: MarkdownItexadded some examples <a href="https://ncatlab.org/nlab/revision/diff/core/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/core/9">v9</a>, <a href="https://ncatlab.org/nlab/show/core">current</a>

   added some examples

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 2nd 2020
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   Author: Urs
   Format: MarkdownItexThanks for contributing. Let's make such lists of examples into bullet-item lists, for ease of discerning them, like so: * Given a [[preorder|preordered set]], regarded as a category, taking its core is the same as partitioning the set into equivalence classes of the preorder. * A combinatorial [[species]] is defined as a [[presheaf]], that is, a contravariant functor to Set, on the core of [[FinSet]]. Your last line added here was: > Every groupoid has a contravariant functor to itself. It preserves the objects and sends the arrows to their inverses. But I don't see how that is an example for the page "core"? <a href="https://ncatlab.org/nlab/revision/diff/core/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/core/10">v10</a>, <a href="https://ncatlab.org/nlab/show/core">current</a>

   Thanks for contributing.

   Let’s make such lists of examples into bullet-item lists, for ease of discerning them, like so:

     * Given a [[preorder|preordered set]], regarded as a category, taking its core is the same as partitioning the set into equivalence classes of the preorder.
   
     * A combinatorial [[species]] is defined as a [[presheaf]], that is, a contravariant functor to Set, on the core of [[FinSet]].
   

   Your last line added here was:

   Every groupoid has a contravariant functor to itself. It preserves the objects and sends the arrows to their inverses.

   But I don’t see how that is an example for the page “core”?

   diff, v10, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2021
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   Author: Urs
   Format: MarkdownItexgave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of $(n,r)$-categories. Added pointer to * [[Jacob Lurie]], Around Prop. 1.1.14 in: _[[(∞,2)-Categories and the Goodwillie Calculus]]_ ([arXiv:0905.0462](http://arxiv.org/abs/0905.0462)) (all this was previously hinted at only rather indirectly through a pointer to _[[category object in an (infinity,1)-category]]_ towards the end). <a href="https://ncatlab.org/nlab/revision/diff/core/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/core/12">v12</a>, <a href="https://ncatlab.org/nlab/show/core">current</a>

   gave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of $(n,r)$-categories. Added pointer to

   • Jacob Lurie, Around Prop. 1.1.14 in: (∞,2)-Categories and the Goodwillie Calculus (arXiv:0905.0462)

   (all this was previously hinted at only rather indirectly through a pointer to category object in an (infinity,1)-category towards the end).

   diff, v12, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexgave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of $(n,r)$-categories. Added pointer to * [[Jacob Lurie]], Around Prop. 1.1.14 in: _[[(∞,2)-Categories and the Goodwillie Calculus]]_ ([arXiv:0905.0462](http://arxiv.org/abs/0905.0462)) (all this was previously hinted at only rather indirectly through a pointer to _[[category object in an (infinity,1)-category]]_ towards the end). <a href="https://ncatlab.org/nlab/revision/diff/core/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/core/12">v12</a>, <a href="https://ncatlab.org/nlab/show/core">current</a>

   gave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of $(n,r)$-categories. Added pointer to

   • Jacob Lurie, Around Prop. 1.1.14 in: (∞,2)-Categories and the Goodwillie Calculus (arXiv:0905.0462)

   (all this was previously hinted at only rather indirectly through a pointer to category object in an (infinity,1)-category towards the end).

   diff, v12, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexSorry for the duplicate. Am having much trouble with timeouts when saving, as of late.

   Sorry for the duplicate. Am having much trouble with timeouts when saving, as of late.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 28th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a sentence relating to *[[free groupoid]]* also changed the page title from just "core" to "core groupoid", which seems to make better sense as a page title <a href="https://ncatlab.org/nlab/revision/diff/core+groupoid/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/core+groupoid/16">v16</a>, <a href="https://ncatlab.org/nlab/show/core+groupoid">current</a>

   added a sentence relating to free groupoid

   also changed the page title from just “core” to “core groupoid”, which seems to make better sense as a page title

   diff, v16, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeMay 31st 2023
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   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Pierre Gabriel]], [[Michel Zisman]], §1.5.4 of: *[[Calculus of fractions and homotopy theory]]*, Ergebnisse der Mathematik und ihrer Grenzgebiete **35**, Springer (1967) &lbrack;[doi:10.1007/978-3-642-85844-4](https://link.springer.com/book/10.1007/978-3-642-85844-4), [pdf](https://web.math.rochester.edu/people/faculty/doug/otherpapers/GZ.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/core+groupoid/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/core+groupoid/18">v18</a>, <a href="https://ncatlab.org/nlab/show/core+groupoid">current</a>

   added pointer to:

   • Pierre Gabriel, Michel Zisman, §1.5.4 of: Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 35, Springer (1967) [doi:10.1007/978-3-642-85844-4, pdf]

   diff, v18, current

9. • CommentRowNumber9.
   • CommentAuthorJohn Baez
   • CommentTimeOct 7th 2024
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   Author: John Baez
   Format: MarkdownItexThe functor "core" is usually lower case on this page but occasionally written "Core". I made it lower case everywhere. <a href="https://ncatlab.org/nlab/revision/diff/core+groupoid/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/core+groupoid/21">v21</a>, <a href="https://ncatlab.org/nlab/show/core+groupoid">current</a>

   The functor “core” is usually lower case on this page but occasionally written “Core”. I made it lower case everywhere.

   diff, v21, current