Measuring coalgebra

In algebra, a measuring coalgebra of two algebras A and B is a coalgebra enrichment of the set of homomorphisms from A to B. In other words, if coalgebras are thought of as a sort of linear analogue of sets, then the measuring coalgebra is a sort of linear analogue of the set of homomorphisms from A to B. In particular its group-like elements are (essentially) the homomorphisms from A to B. Measuring coalgebras were introduced by Sweedler (1968, 1969).