uconf.morphisms.classical

Classical operad morphisms.

Provides the standard morphisms between classical operads:

• ass_to_com: Ass → Com (augmentation — sends every permutation to the commutative generator).

• lie_to_ass: Lie → Ass (PBW inclusion — sends a Lie bracket to its commutator expansion in the associative operad).

Module Attributes

ass_to_com	Augmentation morphism Ass → Com.
lie_to_ass	PBW inclusion Lie → Ass.

uconf.morphisms.classical.ass_to_com = <uconf.core.morphism.OperadMorphism object>

Augmentation morphism Ass → Com.

Every permutation σ ∈ Ass(n) maps to the unique generator of Com(n).

Parameters:

element (Any)

Return type:

Any

uconf.morphisms.classical.lie_to_ass = <uconf.core.morphism.OperadMorphism object>

PBW inclusion Lie → Ass.

Sends a Lie bracket [x_i, ...] to the corresponding commutator in the associative operad.

Parameters:

element (Any)

Return type:

Any