Let $C$ be a category and $D$ a full subcategory of $[C^{op}, \mathrm{Set}]$. Can we form something like Grothendieck topos generated by $D$? By that I mean some full subcategory $\mathcal{E}$ of $[C^{op},\mathrm{Set}]$ which is a Grothendieck topos containing $D$ and is somewhat universal among those Grothendick topoi (for example, every fully faithful embedding of $D$ into a Grothendieck topos factors through $\mathcal{E}$ or something similar).
2026-03-28 16:57:03.1774717023
Category of sheaves generated by a subcategory?
55 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CATEGORY-THEORY
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