nLab
intertwiner

Idea

The term intertwiner is a synonym for homomorphism of representations/actions/modules.

Notably for linear representations ${\rho }_1$, ${\rho }_2$ of some group or associative algebra $A$ on vector spaces $V_1,V_2$, a linear map $u:V_1\to V_2$ is said to intertwine ${\rho }_1$ with ${\rho }_2$ if for all $a\in A$ we have that

$$u\circ {\rho }_1(a)={\rho }_2(a)\circ u.$$u \circ \rho_1(a) = \rho_2(a)\circ u \,.