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Jun 25, 2012 at 19:12 comment added Benjamin Steinberg You do not need injectivity if you want to work with simplicial sets. If an order preserving map crushes to vertices of a simplex, then you get a degenerate simplex. This is why in my opinion it is preferable to work with simplicial sets rather than $\Delta$-sets.
Jun 25, 2012 at 19:10 vote accept Benjamin Steinberg
Jun 25, 2012 at 19:03 history answered Vidit Nanda CC BY-SA 3.0