You confuse objectivity with real objects and theoretic with subjective.
Ti is objective, although not related to things. The only truly factual information types are Se and Te. But Ti, compared to Te is rather theoretical, as you know, there's where you confuse it with "subjective". Please read the definitions of these 4 terms and you understand without any further effort (if you're really willing to understand).
This is your main problem, you make too many
equivocation fallacies and I told you previously that you'd better use Bodies/Fields for your sake, because the term "object" is too similar to "objectivity" although they have little meaningful connection, especially talking about psychic functions where such mistake make you misunderstand completely the whole picture, the names are just keywords. What's your justification to associate the "Bodies" partition with "objectivity"?
Did you read the actual descriptions of these dichotomies, did you read Sedykh's article?? You never explained that, because it's a *fact* that "obj*" = "obj*"?
Please read what objects mean and note the "news" that humanity has discovered abstract objects a long time ago.
And read that damn article and descriptions, don't pretend that you miss them and don't reinvent Socionics.