Coalgebra(R, MxM)ΒΆ

tensor.spad line 441

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
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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
opposite?: (%, %) -> Boolean
from AbelianMonoid
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule R

Module R

RightModule R

SetCategory