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The filtered limit is typo of filtered colimit peter <a href="https://ncatlab.org/nlab/revision/diff/pro-%C3%A9tale+morphism+of+schemes/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/pro-%C3%A9tale+morphism+of+schemes/4">v4</a>, <a href="https://ncatlab.org/nlab/show/pro-%C3%A9tale+morphism+of+schemes">current</a>
The filtered limit is typo of filtered colimit
peter
diff, v4, current
It should be cofiltered limit actually. crystalline <a href="https://ncatlab.org/nlab/revision/diff/pro-%C3%A9tale+morphism+of+schemes/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/pro-%C3%A9tale+morphism+of+schemes/5">v5</a>, <a href="https://ncatlab.org/nlab/show/pro-%C3%A9tale+morphism+of+schemes">current</a>
It should be cofiltered limit actually.
crystalline
diff, v5, current