Para-Associative Operation

A Ternary Operation [ , , ] : A A A A : 𝐴 𝐴 𝐴 𝐴 [-,-,-]:A\to A\to A\to A is para-associative if it satisfies the following equations:

Note that the term "pseudoassociative" is often used in the literature; we avoid this to prevent confusion with things like "pseudofunctor".