In nLab we read:
Set is the discrete object classifier in the category Grpd of groupoids and functors.
But this is far above my head, could you say in more simple terms what is the relation? Set is a subcategory of Grpd? Set is an object of Grpd?
2026-03-29 18:31:32.1774809092
What is the precise relation between the category Set and the category Grpd?
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The wording of the nLab article was confusing (and arguably incorrect). What was meant is that the core groupoid of the category of sets is the discrete object classifier in $\mathbf{Grpd}$. Explicitly, the core groupoid is $\mathbf{Set}_{\text{bij}}$, the category of sets and bijections, which we view as an object of $\mathbf{Grpd}$. The wording in the article has since been updated to clarify this.