diagrams.CubeDiagram

class rewalt.diagrams.CubeDiagram(ambient)

Bases: Diagram

Subclass of Diagram for diagrams whose shape is an oriented cube.

The methods of this class provide an implementation of the structural maps of a cubical set with connections.

Methods

cube_connection(k, sign)	Returns one of the connections of the cube.
cube_degeneracy(k)	Returns one of the degeneracies of the cube.
cube_face(k, sign)	Returns one of the faces of the cube.

cube_face(k, sign)

Returns one of the faces of the cube.

This is, by definition, the pullback of the diagram along self.shape.cube_face(k, sign).

Parameters

• k (int) – Index of the face, ranging from 0 to self.dim - 1.

• sign (str) – Side: '-' or '+'.

Returns

cube_face – The face.

Return type

Diagram

Raises

ValueError – If the index is out of range.

cube_degeneracy(k)

Returns one of the degeneracies of the cube.

This is, by definition, the pullback of the diagram along self.shape.cube_degeneracy(k).

Parameters

k (int) – The index of the degeneracy, ranging from 0 to self.dim.

Returns

cube_degeneracy – The degeneracy.

Return type

Diagram

Raises

ValueError – If the index is out of range.

cube_connection(k, sign)

Returns one of the connections of the cube.

This is, by definition, the pullback of the diagram along self.shape.cube_connection(k, sign).

Parameters

• k (int) – Index of the connection, ranging from 0 to self.dim - 1.

• sign (str) – Side: '-' or '+'.

Returns

cube_face – The connection.

Return type

Diagram

Raises

ValueError – If the index is out of range.