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Complexes :: ComplexMap

ComplexMap -- the class of all maps between chain complexes

Description

A map of chain complexes $f \colon C \rightarrow D$ of degree $d$ is a sequence of maps $f_i \colon C_i \rightarrow D_{d+i}$. No relationship between the maps $f_i$ 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.