The Homotopic Category
Let Y and Z be simplicial sets, and let Hom (Y, Z) be the complex defined in II, 2.5.3. A vertex ofHom (Y, Z) is a morphism f: Y→Z. If f and g are two vertices, a 1-simplex h of Hom(Y, Z) such that d 1 h= f and d 0 h=g is a morphism h: ∆ × Y→Z which makes the following triangles commutative (Fig. 25).
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