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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 23rd 2012

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

• CommentRowNumber2.
• CommentAuthorYuxi Liu
• CommentTimeJul 1st 2020

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 2nd 2020

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]].


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”?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeDec 29th 2021

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

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

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeDec 29th 2021

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

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 29th 2021

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