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The ordinal category of all ordinal numbers with monotonic morphisms is the basis for simplicial techniques: a contravariant functor from the ordinal category to another category is called simplicial object.

Walk-through to Morel-Voevodsky A¹-homotopy theory, page 48-50

5 February, 2010 in category Walkthrough to Morel-Voevodsky A1-homotopy theory, english by Konrad.

Chapter 2.1. Homotopy theory of simplicial sheaves: The simplicial model category structure. Discussion of 1.2, 1.3, 1.4, 1.5, 1.6, 1.8, 1.9, 1.10.