A left (right) corepresentation is a synonym for a left (right) coaction of a coalgebra (comonoid) in one of the monoidal categories which have linear, and possibly, functional connotation; e.g. in the context of topological vector spaces.
There is however also another meaning of a corepresentation for a Leibniz algebra.
Both a representation and a corepresentation of a right Leibniz -algebra involve a -module and two -linear maps “actions” and with 3 axioms.
for and for .
If the two “actions” are symmetric, i.e. for all , then all the 6 axioms of representation or corepresentation are equivalent. If is underlying a Leibniz algebra then an action of on is by definition symmetric, hence all the 6 equivalent conditions hold.