I apologize for this naive question, I believe it's somewhere in HA but I just can't find it.
For symmetric monoidal category $C$, consider $A\in CAlg(C)$, and $M,N\in Mod_A(C)$, we can formulate the relative tensor product of $M$ and $N$ over $A$ by Bar construction, and if we regard $M\in {}_ABMod_{1}(C)$, and $N\in {}_1BMod_{A}(C)$, then we have $M\otimes N\in {}_{A}BMod_{A}(C)$, and also $A$ is canonically an $(A,A)$ bimodule, so they can be regarded as $A\otimes A$ modules, and we have the relative tensor product over $(M\otimes N)\otimes_{A\otimes A}A$.
Intuitively this gives relative tensor product over $A$: $M\otimes_A N$, if we are in the classical case of a ring $A$ and $A$ modules $M,N$, then $(M\otimes N)\otimes_{A\otimes A} A$ makes $am\otimes n\cong m\otimes an\cong a(m\otimes n)$, but how to formulate this rigorously in higher algebra, I tried to prove that they are equivalent at the level of Bar constructions, or by the universal property of relative tensor product, but end in failure.
Any references or suggestions are very welcome.
