# Does the homology, homotopy, and geometric realization functors of a simplicial group preserve colimits?

Given a based simplicial group, you can find its reduced homology with coefficients in a field, homotopy, and geometric realization. These are functors. If I have a free product of based simplicial groups, does these associated functors split into coproducts? More generally, does these functors preserve colimits?

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@Exterior Nowhere, because it doesn't. Consider the pushout that constructs $S^1$ as the interval with its endpoints glued. $H_1$ does obviously not preserve that pushout. – archipelago Feb 1 at 16:24