Does it make any difference, in the definition of a reflective subcategory, if the reflection induced by $f$ goes directly to the codomain of $f$ or if we, on the contrary, insert a reflection between codomain of $f$ and codomain of the reflection induced by $f$. In the former case it is understood that $f$ lies in the entire category while in the latter case that $f$ targets to the reflective part.
EDIT Here $f$ is that "arbitrary" morphism from which domain leads the reflection (which will be the same if any other $g$ has the same domain) and which induces the unique morphism in the reflective subcategory which codomain leads (according to my problem) directly to the codomain of $f$ or [this is the question] to the codomain of another reflection. For your second query I cannot write which one of these 2 definitions I have in mind since I'm asking about their relationship. So my question is, which definition from the two is correct, in case that they are not equivalent.
EDIT 2
If this EDIT 2 won't do the job I'll draw a picture and scan it in the next week. My question is, shall I postcompose any such $f$ with the reflection pertaining to $f$'s codomain, or is it equivalently enough that $f$ has the codomain in the reflective subcategory without post-composing it ?
EDIT 3 Drawing has been done:
EDIT 4 Obviously, $(2)\Longrightarrow(1)$.