# coinvariant

Let $V$ be a comodule with a right coaction $t\colon V\to V\otimes A$ of a coalgebra $A$. An element $v\in V$ is right coinvariant if

 $t(v)=v\otimes\mathord{\mathrm{1\!\!\!\>I}}_{A}.$ (1)

The set of coinvariants of $A$ is a sub-comodule with the trivial coaction of $A$. The sub-comodule of right (or left) coinvariants of $V$ is sometimes denoted by $V^{\mathrm{co}A}$ (or ${}^{\mathrm{co}A}V$).

Title coinvariant Coinvariant 2013-03-22 13:57:40 2013-03-22 13:57:40 mhale (572) mhale (572) 5 mhale (572) Definition msc 16W30