# coinvariant

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

$$t(v)=v\otimes {1\mathrm{I}}_{A}.$$ | (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 |
---|---|

Canonical name | Coinvariant |

Date of creation | 2013-03-22 13:57:40 |

Last modified on | 2013-03-22 13:57:40 |

Owner | mhale (572) |

Last modified by | mhale (572) |

Numerical id | 5 |

Author | mhale (572) |

Entry type | Definition |

Classification | msc 16W30 |