# Coalgebra(R, MxM)ΒΆ

A coalgebra A over a ring is an `R`-module with a coassociative comultiplication from A to the tensor product of A with itself and which possesses a counit.

0: %

from AbelianMonoid

*: (%, 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

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
coproduct: % -> MxM

`coproduct(x)` computes the coproduct of an element `x`

counit: % -> R

`counit(x)` evaluates the counit at an element `x`

latex: % -> String

from SetCategory

opposite?: (%, %) -> Boolean

from AbelianMonoid

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

SetCategory