In the category Δ o Ens , of the simplicial sets, there exists a Unit interval : the simplicial set Δ[1], with extremities e i : Δ[0] → Δ[1] (i = 0, 1) ([1], [2] ). On the other hand, since in Δ o Ens, the products are representable and Δ[0] is a final object, these exists in Δ o Ens, a completely natural notion of homotopy : two arrows f o , f 1 : X → Y are simply homotopic if there is an arrow F which makes the following diagram commutative.
