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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.

5 votes

On the construction of the simplicial category $\Delta$

The construction I think you are looking for is due to Benabou and given at the end of the paper "Some remarks on free monoids in a topos", LNM1488, Category theory (Como, 1990), 20–29. Here is a sum …
John Bourke's user avatar