symmetric monoidal (∞,1)-category of spectra
In deformation quantization of Poisson manifolds the commutative product $\cdot$ of the commutative algebra of functions is replaced by a noncommutative associative product. This is often called a star product and denoted “$\star$”.
An archetypical example is the Moyal star product that deforms the function algebra on a Poisson vector space, and sometimes “star product” is by default understood to be a Moyal star product.
More recently also nonassociative “star products” have been proposed to be of interest.