What does homomorphism mean in the GLOVE paper?

Question

It is mentioned in the GloVe: Global Vectors for Word Representation. It says:

where $w_i$, $w_j$ and $\tilde{w}_k$ are all word vectors and $F$ is just an unknown function. The author then assumes $F$ as $exp$. What is homomorphism exactly? Why equation (4) can make $F((w_i - w_j)^T\tilde{w}_k)$ homomorphism?

Answer 1

copying verbatim from Wikipedia

A homomorphism is a map between two algebraic structures of the same type (that is of the same name), that preserves the operations of the structures. This means a map ${\displaystyle f:A\to B}$ between two sets $A$, $B$ equipped with the same structure such that, if $∗$ is an operation of the structure (supposed here, for simplification, to be a binary operation), then $${\displaystyle f(x*y)=f(x)*f(y)}$$ for every pair $x, y$ of elements of $A$