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Answer by Buschi Sergio for Adjunction between Pro and Ind Completions

No a answere but a specification and description of the issue (too long for a comment).The free cocompletion property of $Ind(\mathcal{C})$ dont use the hypothesis "$\mathcal{C}$ has finite colimits"....

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Adjunction between Pro and Ind Completions

Hi,Let $\mathcal{C}$ be a small category with finite limits and finite colimits. The Ind-completion $Ind(\mathcal{C})$ is a locally finitely presentable category which is the free cocompletion of...

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