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Complexes :: ComplexMap

ComplexMap -- the class of all maps between chain complexes

Description

A map of chain complexes f : C →D of degree d is a sequence of maps fi : Ci →Dd+i. No relationship between the maps fi and and the differentials of either C or D is assumed.

The set of all maps from C to D form the complex Hom(C,D) where Hom(C,D)d consists of the maps of degree d.

The usual algebraic operations are available: addition, subtraction, scalar multiplication, and composition. The identity map from a chain complex to itself can be produced with id. An attempt to add (subtract, or compare) a ring element to a chain complex will result in the ring element being multiplied by the appropriate identity map.

See also

Functions and methods returning a map of complexes :

Methods that use a map of complexes :

For the programmer

The object ComplexMap is a type, with ancestor classes HashTable < Thing.