Cat::Monoid
-- the category of
monoidsCat::Monoid
represents the category of monoids.
Cat::Monoid()
Cat::SemiGroup
Cat::Monoid
is a non-abelian semi-group with a
neutral element one (dom::one
) according to the group
operation *
(_mult
).Must hold the neutral element according to the operation
*
.
_invert(dom x)
x
according to the operation
*
or FAIL
if
no inverse exists.isone(dom x)
x
is equal to one. Uses the method
"equal"
if this domain has not the axiom Ax::normalRep
._power(dom x, DOM_INT
n)
dom::one
if n
is 0 and the
n
-fold product of x
if n
is
positive. If n
is negative then x
is
inverted. If no inverse exists FAIL
is returned, otherwise the
-n
-fold product of the inverse.