Homotopy Type Theory
dependent type

A dependent type is a family of types indexed by - “depending on” - values of another type.

Given a type $A$ in a universe of types $\mathcal{U}$, a dependent product type (or ‘pi-type’) $B$ is a family of types:

$$\Pi_{(a:A)}B(a)$$

Similarly, a dependent sum type (or ‘sigma-type’) $B$ is a family of types:

$$\Sigma_{(a:A)}B(a)$$

See also

‘Dependent type’ on the nLab wiki.

category: type theory