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Is $Tor_A(k,k)$ a bicommutative Hopf algebra?

Let $A$ be a commutative (or graded commutative) algebra over a field $k.$ In some sources, such as Mcleary's book on spectral sequences, Corollary 7.12, pg. 248, it is claimed that $\text{Tor}_A(k,k)$...
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