uconf.core.cooperad

Typing protocols for cooperad-like objects used in this project.

Note

This package works exclusively with connected cooperads, i.e. cooperads C satisfying C(0) = 0 and C(1) = k (the ground field, spanned by the counit). Connectedness implies that every internal vertex of a tree in the cobar construction has arity >= 2, which bounds the number of vertices in arity n by n - 1. All concrete models and wrappers in this package are connected.

Module Attributes

CooperadLike

Type alias for accepted cooperad inputs (class or factory instance).

Classes

CooperadComponent(n, base_ring)	Structural contract for one fixed-arity cooperad component.
CooperadFactory(*args, **kwargs)	Structural contract for cooperad factories and wrappers.

class uconf.core.cooperad.CooperadComponent(n, base_ring)

Bases: ComponentProtocol, Protocol

Structural contract for one fixed-arity cooperad component.

Parameters:

n (int)

factory: type[CooperadComponent] | CooperadFactory

Reference to the parent cooperad factory, used for printing and error messages.

static counit(x)

Returns the counit evaluation on x.

Parameters:

x (Element)

Return type:

object

static unit_key()

Returns the basis key of the counit generator in arity 1.

Return type:

Any

static reduced(x)

Projects x to the reduced part (kills counit in arity 1).

Parameters:

x (Element)

Return type:

Element

static infinitesimal_cocompose(x, i, m, n)

Returns the partial cocomposition in slot i, arities (m, n).

Parameters:

• x (Element)

• i (int)

• m (int)

• n (int)

Return type:

Iterable[tuple]

class uconf.core.cooperad.CooperadFactory(*args, **kwargs)

Bases: Protocol

Structural contract for cooperad factories and wrappers.

counit(x)

Returns the counit evaluation on x.

Parameters:

x (Any)

Return type:

object

unit_key()

Returns the basis key of the counit generator in arity 1.

Return type:

Any

reduced(x)

Projects x to the reduced part.

Parameters:

x (Any)

Return type:

Any

infinitesimal_cocompose(x, i, m, n)

Returns the partial cocomposition in slot i.

Parameters:

• x (Any)

• i (int)

• m (int)

• n (int)

Return type:

Any

uconf.core.cooperad.CooperadLike: TypeAlias = type[uconf.core.cooperad.CooperadComponent] | uconf.core.cooperad.CooperadFactory

Type alias for accepted cooperad inputs (class or factory instance).