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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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A map between direct limits

Let $C$ be a category which has all small colimits. I have the following situation: $\{A_i\}_{i \in I}$ and $\{B_j\}_{j \in J}$ are two directed systems in $C$, with transition maps $\alpha_{i_1,i_2 …
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