symmetric monoidal (∞,1)-category of spectra
A differential algebra is an associative algebra $A$ equipped with a derivation $d \colon A \to A$, typically required to satisfy $d \circ d = 0$.
If $A$ is a field one accordingly speaks of a differential field.
If $A$ is a graded algebra and $d$ is of degree 1 one speaks of a differential graded algebra.
Etc.