nLab finite type

The term “finite type” may refer to:

• In algebra, homological algebra and rational homotopy theory:

  objects of finite type.

• In homotopy theory:

  finite homotopy type or π-finite homotopy type

• In rational homotopy theory also:

  with finite dimensional rational cohomology in each degree (“rational finite type”)

• In type theory:

  types of the kind of finite sets (see at family of finite types and inductive family)

  also pi-finite types, type of finite types

Related concepts:

• finite set, profinite set

• finite number

• finite object

• finitely generated object, finitely presented object

• (fully-)dualizable object

  perfect module

• compact object

• finite category, finite graph

• finite CW-complex, finite spectrum