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added at core the remark that the core is right adjoint to the forgetful functor $Grpd \to Cat$.
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”?
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).
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).
Sorry for the duplicate. Am having much trouble with timeouts when saving, as of late.
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
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