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
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