A groupoid is a semigroupoid where inverse are defined for all elements, and thus left and right identity elements such that:
A left partial action of a semigroupoid G
on P
is the implementation of
a method partialActl(g, p)
, or g ?|+|> p
returning Opt[P]
, such that:
A partial action is the combination of left and right partial actions, providing:
A right partial action of a semigroupoid G
on P
is the implementation of
a method partialActr(p, g)
, or p <|+|? g
returning Opt[P]
, such that:
A semigroupoid is any set A
with a partial binary associative operation (partialOp
),
which is associative in the following sense: if f,g,h are elements of the semigroupoid
such that either:
(i) f |+|? g is defined and g |+|? h is defined
(ii) f |+|? g is defined and (f |+|? g).