According to the article: every c.e.language over $\Sigma^*$can be formed by homomorphism from a Dyck language over $\Sigma^{'}$ intersection with a minimal linear language over $\Sigma^{'}$ to the Kleene closure $\Sigma^*$ over a alphabet.

Now we know, intersection between languages is parallel to series connection of the corresponding Turing Machines. Then what does homomorphism between languages mean to the correspoding Turing Machines?

Partially it seemingly means merge of computational paths,