We show that natural transformations play the role of homotopy for (covariant) functors. Homotopic functors are shown to induce identical maps between the homology groups of categories. For a space X, there is an associated category AS(X). We show that the classifying space of AS(X) has the same homotopy type as X if X is a CW complex. Moreover, we prove that, for CW complexes X and Y, f and g:X-+ Y are homotopic if and only if AS(f) and AS(g) are.