On kan's condition (1972)
In the category    Δo Ens   ,   of the simplicial sets, there exists a "Unit interval" : the simplicial set   Δ[1],     with extremities   εi : Δ[0] → Δ[1] (i = 0, 1) ([1], [2] ). On the other hand, since in   Δo Ens,       the products are representable and    Δ[0]    is a final object, these exists in    Δo Ens,    a completely natural notion of homotopy :  two arrows fo , f1 : X → Y are "simply homotopic" if there is an arrow   F   which makes the following diagram commutative.