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Let $DGA(R)$ be the category of differential graded algebras (with unit) over a commutative ring $R$. I often read that this category obviously has all filtered colimits. Can someone explain them?

Or can somebody explain direct limits in this category if that's easier?

Thank you!

tzpl11
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  • Just a side remark: in any category, filtered colimits and direct limits coincide (a proof is e.g. in Locally Presentable and Accessible Categories, Thm 1.5, by Adámek and Rosický). – Pavel Čoupek Sep 28 '16 at 22:51

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