symmetric monoidal (∞,1)-category of spectra
If the -algebra is equipped with an -algebra homomorphism the other way round,
then it is called an augmented algebra.
In Cartan-Eilenberg this is called a supplemented algebra.
If is a variety over an algebraically closed field and is a closed point, then the local ring naturally has the structure of an augmented -algebra. The augmentation map is the evaluation map, and the augmentation ideal is the maximal ideal of .