Pet peeve: The word "just" when used to gloss over something with the author don't know how to explain. Using "just" shift the burden from the author to the reader, since it signals it is the readers fault if they don't understand.
> A homomorphism is just a structure preserving map. In fact, a functor is just a homomorphism between categories as it preserves the original category's structure under the mapping.
How about removing the "just":
> A homomorphism is a structure preserving map. A functor is a homomorphism between categories as it preserves the original category's structure under the mapping.
Much clearer. Although most readers would now ask what "structure" and "structure preserving" means, since this is never explained.
> A homomorphism is just a structure preserving map. In fact, a functor is just a homomorphism between categories as it preserves the original category's structure under the mapping.
How about removing the "just":
> A homomorphism is a structure preserving map. A functor is a homomorphism between categories as it preserves the original category's structure under the mapping.
Much clearer. Although most readers would now ask what "structure" and "structure preserving" means, since this is never explained.