Given a size pair is a manifold is an arbitrary real continuous function-th size functor,, is the functor is the category is the category of Abelian groups equal to the morphism,

is a Morse function − trees.

The concept of size functor was introduced as an extension to homology theory and category theory of the idea of size function. The main motivation for introducing the size functor originated by the observation that the size function.

The concept of size functor is strictly related to the concept of persistent homology group, studied in persistent homology-th persistent homology group coincides with the image of the homomorphism.

See also

• Size theory

• Size function

• Size homotopy group

• Size pair

References