If a group $G$ acts on an affine variety $X$, and $W$ is a $G$-module, a covariant on $X$ with values in $W$ is a regular function $X\to V$ W$ which is $G$-equivariant.
In the special case in which $G=\mathrm{SL}(V)$ is the special linear group on a vector space $V$, $X=\mathrm{Pol}_{d_1}(V)\otimes\cdots\otimes\mathrm{Pol}_{d_s}(V)$ and $W=\mathrm{Pol}_{d}(V)$, with natural actions of $G$, a covariant $X\to W$ is called a concomitant of degree $d$. The canonical example of a concomitant is the resultant $R(f_1,\dots,f_s)$ of $s$ homogeneous polynomial functions $f_1\in\mathrm{Pol}_{d_1}(V), \dots, f_s\in\mathrm{Pol}_{d_s}(V)$ of degrees $d_1,\dots,d_s$, which has degree $0$. A simpler example is the Jacobian of $n$ homogeneous forms in $n$ variables.
