Let be comonoids in a monoidal category . A - bicomodule is an object in , with left -coaction and right -coaction which commute in the sense that
(\lambda_C\otimes id_D)\circ\rho_D = (id_C\otimes \rho_D)\circ \lambda_C.
Typical cases are when is the category of -modules where is a commutative unital ring (the comonoids are then -coalgebras), and the more general case of bicomodules over corings, where is the category of -bimodules where is a possibly noncommutative ring.
There is an operation of cotensor product for bicomodules over coalgebras/corings; however it is not associative in general, unlike the tensor product of bimodules over rings!
Revised on October 11, 2011 01:26:20
by Todd Trimble