If $C$ is a category then an ind-object$x\in Ind(C)$ is a strict ind-object (alias essentially monomorphic ind-object) if it can be represented in $Ind(C)$ as (the apex of) a colimit of a small filtered diagram (whose objects are in $C$ and) whose morphisms are specifically monomorphisms in $C$.

David Blanc, Colimits for the pro-category of towers of simplicial sets, Cahiers de Topologie et Géométrie Différentielle Catégoriques (1996) Volume: 37, Issue: 4, page 258-278 (numdam)

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