Coalgebra(R, MxM)

tensor.spad line 447 [edit on github]

• R : CommutativeRing
• MxM : Module(R)

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.

* : (%, R) -> %

from RightModule(R)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(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")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

SetCategory

CoercibleTo(OutputForm)

AbelianMonoid

RightModule(R)

AbelianSemiGroup

BiModule(R, R)

Module(R)

LeftModule(R)

BasicType

AbelianGroup