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Usually one writes $X_\bullet$ both for simplicial sets and for semisimplicial sets. But this is potentially confusing if I want to consider maps $X_\bullet\to Y_\bullet^\text{forget}$ in the category of semisimplicial sets where $Y_\bullet$ is a simplicial set. Is there a standard way to notationally distinguish simplicial sets and semisimplicial sets? (so that from the unadorned $X_\bullet$ and $Y_\bullet$ one could tell they live in different categories)

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Semisimplicial sets are rather nonstandard, so I'd say 'no'. –  Fernando Muro May 31 '13 at 20:06
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