uconf.core.morphism

Morphisms of dg-operads and pullback algebras.

An operad morphism f: P → Q is a collection of linear maps f_n: P(n) → Q(n) satisfying:

  • Unit: f_1(id_P) = id_Q

  • Composition: f(x ∘_i y) = f(x) ∘_i f(y)

  • Equivariance: f(x·σ) = f(x)·σ

  • Chain map: f(∂x) = ∂f(x)

Given a Q-algebra (A, γ^Q) and a morphism f: P → Q, the pullback f^*(A) is the P-algebra (A, γ^P) with structure map γ^P(p; a_1,…,a_n) = γ^Q(f(p); a_1,…,a_n).

Classes

OperadMorphism(source, target, on_element)

A morphism f: P → Q of dg-operads.
class uconf.core.morphism.OperadMorphism(source, target, on_element)[source]

Bases: object

A morphism f: P → Q of dg-operads.

Parameters

sourceOperadLike

Source operad (class or factory).

targetOperadLike

Target operad (class or factory).

on_elementcallable

A function mapping elements of P(n) to elements of Q(n). Must be linear in the element.

Parameters: