We characterize, over an arbitrary ground field, when a tensor product of modules is strong cotilting, and deduce that the tensor product of Cohen–Macaulay algebras is again Cohen–Macaulay, affirmatively answering a question of Auslander and Reiten. We further prove that a Cohen–Macaulay algebra with dualizing bimodule W and little finitistic injective dimension d is Iwanaga–Gorenstein if and only if W is a (d+1)-syzygy, equivalently, its Cohen–Macaulay category coincides with the category of n-syzygies for some n>d. This identifies the precise threshold beyond the degree-d condition in view of the counterexamples of Chan, Iyama, and Marczinzik. This is a joint work with Zhaoyong Huang.