API Reference
SimplicialFunctor
SimplicialFunctor.__getitem__()
SimplicialFunctor.__init__()
SimplicialFunctor.add()
SimplicialFunctor.create_coalgebra_structure_map()
SimplicialFunctor.create_morphism()
SimplicialFunctor.create_object()
SimplicialFunctor.create_triangle()
SimplicialFunctor.define_degeneracy()
SimplicialFunctor.define_face()
SimplicialFunctor.degeneracy()
SimplicialFunctor.diagnose_partial_structure()
SimplicialFunctor.face()
SimplicialFunctor.find_horns()
SimplicialFunctor.get_endofunctor_trajectory()
SimplicialFunctor.has_lift()
SimplicialFunctor.load_state_dict()
SimplicialFunctor.register_endofunctor_update()
SimplicialFunctor.state_dict()
SimplicialFunctor.verify_simplicial_identities()
Simplex0
Simplex0.dim
Simplex0.basis_id
Simplex0.__deepcopy__()
Simplex0.__eq__()
Simplex0.__hash__()
Simplex0.__init__()
Simplex0.__setattr__()
Simplex0.id
Simplex0.level
Simplex0.name
Simplex0.payload
Simplex1
Simplex1.morphism
Simplex1.__call__()
Simplex1.__eq__()
Simplex1.__hash__()
Simplex1.__init__()
Simplex1.codomain
Simplex1.components
Simplex1.degeneracy()
Simplex1.domain
Simplex1.eval()
Simplex1.face()
Simplex1.id
Simplex1.level
Simplex1.name
Simplex1.payload
Simplex1.to()
SimplexN
SimplexN.components
SimplexN.__eq__()
SimplexN.__hash__()
SimplexN.__init__()
SimplexN.degeneracy()
SimplexN.face()
SimplexN.id
SimplexN.level
SimplexN.name
SimplexN.payload
FuzzySet
FuzzySimplicialSet
KanComplexVerifier
KanComplexVerifier.__init__()
KanComplexVerifier.get_kan_complex_status()
KanComplexVerifier.suggest_improvements()
KanComplexVerifier.verify_all_conditions()
create_model()
get_training_components()
get_advanced_components()
version()
info()
status()
list_components()
CallbackManager
EarlyStopping
SimplicialObject
Simplex2
MapType
HornError
IntegratedFuzzySet
IntegratedSimplex
IntegratedFuzzySimplicialSet
IntegratedCoalgebra
TConorm
FuzzyElement
create_fuzzy_simplex()
create_fuzzy_simplicial_set_from_data()
merge_fuzzy_simplicial_sets()
KanConditionType
KanConditionResult
FCoalgebra
CoalgebraHomomorphism
Bisimulation
GenerativeCoalgebra
CoalgebraCategory
Endofunctor
PowersetFunctor
StreamFunctor
NeuralFunctor
create_llm_coalgebra()
create_diffusion_coalgebra()
create_transformer_coalgebra()
GeneralizedMetricSpace
EnrichedCategory
YonedaEmbedding
MetricYonedaApplications
UniversalRepresenter
create_llm_metric_space()
create_causal_metric_space()
get_verification_components()
MetricTracker
create_gaia_llm()
set_seed()
Core Components
SimplicialObject.level
SimplicialObject.name
SimplicialObject.payload
SimplicialObject.id
SimplicialObject.__init__()
Simplex2.components
Simplex2.__eq__()
Simplex2.__hash__()
Simplex2.__init__()
Simplex2.degeneracy()
Simplex2.f
Simplex2.face()
Simplex2.g
Simplex2.h
Simplex2.horn_type()
Simplex2.id
Simplex2.is_inner_horn()
Simplex2.is_outer_horn()
Simplex2.level
Simplex2.name
Simplex2.payload
MapType.FACE
MapType.DEGENERACY
MapType.__contains__()
MapType.__getitem__()
MapType.__iter__()
MapType.__len__()
HornError.__init__()
HornError.add_note()
HornError.args
HornError.with_traceback()
IntegratedFuzzySet.__init__()
IntegratedFuzzySet.alpha_cut()
IntegratedFuzzySet.get_membership()
IntegratedFuzzySet.initialize()
IntegratedFuzzySet.merge_with()
IntegratedFuzzySet.support()
IntegratedFuzzySet.update()
IntegratedFuzzySet.validate()
IntegratedSimplex.__class_getitem__()
IntegratedSimplex.__init__()
IntegratedSimplex.degeneracy_map()
IntegratedSimplex.dimension
IntegratedSimplex.face_map()
IntegratedSimplex.verify_simplicial_identities()
IntegratedFuzzySimplicialSet.__init__()
IntegratedFuzzySimplicialSet.add_simplex()
IntegratedFuzzySimplicialSet.get_membership()
IntegratedFuzzySimplicialSet.initialize()
IntegratedFuzzySimplicialSet.merge_with()
IntegratedFuzzySimplicialSet.update()
IntegratedFuzzySimplicialSet.validate()
IntegratedCoalgebra.__class_getitem__()
IntegratedCoalgebra.__init__()
IntegratedCoalgebra.evolve()
IntegratedCoalgebra.initialize()
IntegratedCoalgebra.is_bisimilar()
IntegratedCoalgebra.iterate_dynamics()
IntegratedCoalgebra.update()
IntegratedCoalgebra.validate()
TConorm.apply()
TConorm.MAXIMUM
TConorm.PROBABILISTIC
TConorm.LUKASIEWICZ
TConorm.__contains__()
TConorm.__getitem__()
TConorm.__iter__()
TConorm.__len__()
FuzzyElement.__init__()
FuzzyElement.element
FuzzyElement.membership
KanConditionType.INNER_HORN_FILLING
KanConditionType.OUTER_HORN_FILLING
KanConditionType.LIFTING_PROPERTY
KanConditionType.FIBRATION_CONDITION
KanConditionType.HOMOTOPY_EXTENSION
KanConditionType.__contains__()
KanConditionType.__getitem__()
KanConditionType.__iter__()
KanConditionType.__len__()
KanConditionResult.__init__()
KanConditionResult.error_message
KanConditionResult.condition_type
KanConditionResult.simplex_id
KanConditionResult.simplex_name
KanConditionResult.horn_index
KanConditionResult.satisfied
KanConditionResult.confidence
KanConditionResult.verification_data
CategoryObject
Morphism
Functor
StructureMap
Coalgebra
FuzzyMembership
SimplicialStructure
HornFiller
MessagePasser
TrainingState
GAIAComponent
IntegratedTrainer
compose_morphisms()
create_identity_morphism()
verify_functor_laws()
ComponentRegistry
CommunicationType
BusinessMessage
BusinessUnit
BusinessUnitHierarchy
create_business_hierarchy_from_model()
simulate_organizational_learning()
EndofunctorProtocol
BackpropagationEndofunctor
SGDEndofunctor
CoalgebraMorphism
BisimulationRelation
FinalCoalgebra
create_parameter_coalgebra()
create_stochastic_coalgebra()
create_bisimulation_between_coalgebras()
SimplicialCoalgebra
CategoricalIntegral
End
Coend
Sheaf
Topos
TopologicalEmbedding
CategoricalProbability
create_complete_gaia_system()
SimplicialError
MapConflictError
BasisClashError
FaceExpectationError
SimplicialObjectProtocol
FuzzySetMorphism
FuzzyCategory
FuzzySimplicialFunctor
create_discrete_fuzzy_set()
create_gaussian_fuzzy_set()
create_triangular_fuzzy_set()
SimplexParameters
LocalObjective
HierarchicalMessagePasser
create_triangle_complex()
create_tetrahedron_complex()
id_edge()
Category
SetCategory
GenerativeAICategory
NaturalTransformation
LeftKanExtension
RightKanExtension
MigrationFunctor
FoundationModelBuilder
create_llm_foundation_model()
create_diffusion_foundation_model()
create_multimodal_foundation_model()
HornFillingVerifier
LiftingPropertyVerifier
FibrationVerifier
verify_model_kan_conditions()
create_kan_verification_summary()
FuzzySetAdapter
FuzzySimplicialSetAdapter
CoalgebraAdapter
create_legacy_fuzzy_set()
create_legacy_fuzzy_simplicial_set()
create_legacy_coalgebra()
BasisRegistry
create_synthetic_dataset()
create_xor_dataset()
create_regression_dataset()
FCoalgebra.__class_getitem__()
FCoalgebra.__init__()
FCoalgebra.evolve()
FCoalgebra.is_fixed_point()
FCoalgebra.iterate()
FCoalgebra.name
FCoalgebra.carrier
FCoalgebra.structure_map
FCoalgebra.endofunctor
CoalgebraHomomorphism.__class_getitem__()
CoalgebraHomomorphism.__init__()
CoalgebraHomomorphism.apply()
Bisimulation.__class_getitem__()
Bisimulation.__init__()
Bisimulation.are_bisimilar()
GenerativeCoalgebra.__class_getitem__()
GenerativeCoalgebra.__init__()
GenerativeCoalgebra.evolve()
GenerativeCoalgebra.is_fixed_point()
GenerativeCoalgebra.iterate()
GenerativeCoalgebra.name
GenerativeCoalgebra.carrier
GenerativeCoalgebra.structure_map
GenerativeCoalgebra.endofunctor
CoalgebraCategory.__init__()
CoalgebraCategory.add_coalgebra()
CoalgebraCategory.add_homomorphism()
CoalgebraCategory.compose_morphisms()
CoalgebraCategory.find_bisimulations()
Endofunctor.__class_getitem__()
Endofunctor.apply()
Endofunctor.fmap()
PowersetFunctor.__class_getitem__()
PowersetFunctor.apply()
PowersetFunctor.fmap()
StreamFunctor.__class_getitem__()
StreamFunctor.apply()
StreamFunctor.fmap()
NeuralFunctor.__class_getitem__()
NeuralFunctor.__init__()
NeuralFunctor.apply()
NeuralFunctor.fmap()
GeneralizedMetricSpace.__class_getitem__()
GeneralizedMetricSpace.__init__()
GeneralizedMetricSpace.distance()
EnrichedCategory.__init__()
EnrichedCategory.add_object()
EnrichedCategory.categorical_coproduct()
EnrichedCategory.categorical_product()
EnrichedCategory.has_morphism()
EnrichedCategory.internal_hom()
EnrichedCategory.tensor_product()
YonedaEmbedding.__class_getitem__()
YonedaEmbedding.__init__()
YonedaEmbedding.embed()
YonedaEmbedding.presheaf_distance()
YonedaEmbedding.universal_property()
YonedaEmbedding.verify_isometry()
MetricYonedaApplications.create_image_metric_space()
MetricYonedaApplications.create_neural_embedding_space()
MetricYonedaApplications.create_probability_metric_space()
MetricYonedaApplications.create_text_metric_space()
UniversalRepresenter.__init__()
UniversalRepresenter.compare_objects()
UniversalRepresenter.find_nearest_neighbors()
UniversalRepresenter.represent()
Training & Optimization
OptimizationType
SchedulerType
OptimizationConfig
ModelConfig
DataConfig
TrainingConfig
GAIATrainingConfig
FuzzyDataEncoder
CoalgebraEvolution
HierarchicalCommunication
KanVerification
GAIATrainer
create_gaia_trainer()
CallbackManager.__init__()
CallbackManager.on_train_begin()
CallbackManager.on_train_end()
CallbackManager.on_train_error()
CallbackManager.on_epoch_begin()
CallbackManager.on_epoch_end()
CallbackManager.on_batch_begin()
CallbackManager.on_batch_end()
EarlyStopping.__init__()
EarlyStopping.on_epoch_end()
Utilities
GAIA Training Callbacks
Bases: object
object
Manages training callbacks for GAIA trainer
Called at the beginning of training
Called at the end of training
Called when training encounters an error
Called at the beginning of each epoch
Called at the end of each epoch
Called at the beginning of each batch
Called at the end of each batch
Early stopping callback