Base Change

The BaseChange interface and the BoolToFuzzy and FuzzyToBool changes of enrichment.

base_change

Change of enrichment (change of base) for V-enriched categories.

A lax monoidal functor F: V → W between algebras induces a change-of-base 2-functor from V-Cat to W-Cat. This transforms all morphism tensors by applying F elementwise, changing the enrichment algebra from V to W.

This module provides:

BaseChange (abstract)
├── BoolToFuzzy   — inclusion {0,1} ↪ [0,1]
└── FuzzyToBool   — thresholding [0,1] → {0,1}

BaseChange

Bases: ABC

Abstract change of enrichment from algebra V to algebra W.

Subclasses must implement source, target, and apply_to_values. apply_to_morphism is derived.

source abstractmethod property

source: Algebra

The source algebra V.

target abstractmethod property

target: Algebra

The target algebra W.

apply_to_values abstractmethod

apply_to_values(tensor: Tensor) -> Tensor

Apply the value-level map V → W elementwise.

PARAMETER	DESCRIPTION
tensor	A V-valued tensor. TYPE: Tensor

RETURNS	DESCRIPTION
Tensor	The corresponding W-valued tensor.

Source code in src/quivers/categorical/base_change.py

@abstractmethod
def apply_to_values(self, tensor: torch.Tensor) -> torch.Tensor:
    """Apply the value-level map V → W elementwise.

    Parameters
    ----------
    tensor : torch.Tensor
        A V-valued tensor.

    Returns
    -------
    torch.Tensor
        The corresponding W-valued tensor.
    """
    ...

apply_to_morphism

apply_to_morphism(morph: Morphism) -> ObservedMorphism

Transform a V-morphism to a W-morphism.

Applies the value-level map to the morphism's tensor and returns an observed morphism with the target algebra.

PARAMETER	DESCRIPTION
morph	A morphism enriched over V. TYPE: Morphism

RETURNS	DESCRIPTION
ObservedMorphism	The same morphism re-enriched over W.

Source code in src/quivers/categorical/base_change.py

def apply_to_morphism(self, morph: Morphism) -> ObservedMorphism:
    """Transform a V-morphism to a W-morphism.

    Applies the value-level map to the morphism's tensor and
    returns an observed morphism with the target algebra.

    Parameters
    ----------
    morph : Morphism
        A morphism enriched over V.

    Returns
    -------
    ObservedMorphism
        The same morphism re-enriched over W.
    """
    new_tensor = self.apply_to_values(morph.tensor.detach())

    return observed(
        morph.domain,
        morph.codomain,
        new_tensor,
        algebra=self.target,
    )

BoolToFuzzy

Bases: BaseChange

Inclusion of the boolean algebra into the fuzzy algebra.

The identity map {0, 1} ↪ [0, 1]. Boolean-valued tensors are already valid fuzzy-valued tensors, so this is the identity on tensor values.

apply_to_values

apply_to_values(tensor: Tensor) -> Tensor

Identity: {0,1} values are already in [0,1].

Source code in src/quivers/categorical/base_change.py

def apply_to_values(self, tensor: torch.Tensor) -> torch.Tensor:
    """Identity: {0,1} values are already in [0,1]."""
    return tensor.clone()

FuzzyToBool

FuzzyToBool(threshold: float = 0.5)

Bases: BaseChange

Thresholding from the fuzzy algebra to the boolean algebra.

Applies a threshold: values >= threshold become 1, others become 0. This is a right adjoint to BoolToFuzzy.

PARAMETER	DESCRIPTION
threshold	The threshold value. Must be in (0, 1). Default 0.5. TYPE: float DEFAULT: 0.5

Source code in src/quivers/categorical/base_change.py

def __init__(self, threshold: float = 0.5) -> None:
    if not (0.0 < threshold < 1.0):
        raise ValueError(f"threshold must be in (0, 1), got {threshold}")

    self._threshold = threshold

threshold property

threshold: float

The threshold value.

apply_to_values

apply_to_values(tensor: Tensor) -> Tensor

Threshold: values >= threshold → 1, else → 0.

Source code in src/quivers/categorical/base_change.py

def apply_to_values(self, tensor: torch.Tensor) -> torch.Tensor:
    """Threshold: values >= threshold → 1, else → 0."""
    return (tensor >= self._threshold).float()