# comodule

Let $(A,\Delta,\varepsilon)$ be a coalgebra. A right $A$-comodule is a vector space $V$ with a linear map $t\colon V\to V\otimes A$, called the right coaction, satisfying

 $(t\otimes\mathrm{id})\circ t=(\mathrm{id}\otimes\Delta)\circ t,\qquad(\mathrm{% id}\otimes\varepsilon)\circ t=\mathrm{id}.$ (1)

An $A$-comodule is also referred to as a corepresentation of $A$.