# map -- make a map

## Synopsis

• Usage:
map(Y,X,d) or map(Y,X)
• Inputs:
• Y, an object, such as a ring, module, or chain complex
• X, another object of the same type
• d, a specification, such as a function, list, or matrix, or if omitted, understood to specify the identity map
• Optional inputs:
• Degree => ..., default value null, specify the degree of a map
• DegreeLift => ..., default value null, make a ring map
• DegreeMap => ..., default value null, make a ring map
• Outputs:
• a map to Y from X defined by data d.

## Description

The function map provides a general mechanism for constructing a map (homomorphism) between rings (), modules (), chain complexes (), or between objects in other categories.

See also the function matrix, which focuses on creating new matrices from rectangular arrays of ring elements or matrices.

## For the programmer

The object map is .