Bialgebra(R, MxM)ΒΆ

tensor.spad line 471 [edit on github]

A bialgebra is a coalgebra which at the same time is an algebra such that the comultiplication is also an algebra homomorphism. MxM: Module(R) should be replaced by a more restricted category, but it is not clear at this point which one.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Integer -> %

from NonAssociativeRing

coerce: R -> %

from Algebra R

commutator: (%, %) -> %

from NonAssociativeRng

coproduct: % -> MxM

from Coalgebra(R, MxM)

counit: % -> R

from Coalgebra(R, MxM)

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra R

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

Coalgebra(R, MxM)

CoercibleTo OutputForm

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Module R

Monoid

NonAssociativeAlgebra R

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown