We prove that the integral cohomology algebra of the moment-angle complex ZK [1] is isomorphic to the Tor-algebra of the face ring of simplicial complex K. The proof relies upon the construction of a cellular approximation of the diagonal map ∆: ZK → ZK × ZK. Cellular cochains do not admit a functorial associative multiplication because a proper cellular diagonal approximation does not exist in general. The construction of momentangle
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Baskakov et al. (2004) studied this question.