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

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injectivity of pushout?

We have the following pushout diagram: $$\begin{array}{ccc} \langle X, Y \rangle & \xrightarrow{\alpha} & \mathbb{Z}_a \ast \mathbb{Z}_b \ast \mathbb{Z}_c \ast \mathbb{Z}_d \\ \downarrow \scriptsize{\ …
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