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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
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Isomorphic functors and their images [closed]
Is the following a true statement?
Let $F:\bf{A}\to\bf{B}$ be a functor, and let $\bf{C}$ be a full subcategory of $\bf{B}$ with inclusion functor $I:\bf{C}\to\bf{B}$. If $G:\bf{C}\to {A}$ is a funct …