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 Utilities
Set random seeds for reproducibility