Remark 4.22.4. Let \mathcal{C} be a category. There exists a big category \text{Ind-}\mathcal{C} of ind-objects of \mathcal{C}. Namely, if F : \mathcal{I} \to \mathcal{C} and G : \mathcal{J} \to \mathcal{C} are filtered diagrams in \mathcal{C}, then we can define
There is a canonical functor \mathcal{C} \to \text{Ind-}\mathcal{C} which maps X to the constant system on X. This is a fully faithful embedding. In this language one sees that a diagram F is essentially constant if and only if F is isomorphic to a constant system. If we ever need this material, then we will formulate this into a lemma and prove it here.
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Comment #9768 by Elías Guisado on
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