The answer has to be
Sarah Palin, in a parallel world where she became President of the United States.
First let's cover the basics. The “woman with the wheel” is the person who drives the country, i.e. the person at the very top. She's the head of the armed forces (“high up in the army”). We're told that she “fires the cannon”, i.e. she launches the country's weapons by herself (or at least she presses the button — other people load the cannon for her); this must refer to the atomic bomb, as other weapons are fired entirely by underlings.
So far we have the gender and position, which still leaves quite a few possibilities. We have to use the rest of the riddle to figure out who it is. The start of the riddle is a big clue: it's an “abstraction”, so this is about a fictional world! Furthermore, it's a “nonsensical” one, i.e. a counterfactual one: an alternate world where history proceeded differently.
We have a woman who's “fast”. This could be interpreted in several ways. A common meaning is one who sleeps around, but among politicians, sleeping around is far more common with men than with women. So “fast” must refer to another meaning of the word — tenacious, resistant, not fading with age. I can think of several women who came close to becoming head of state and who fit this description, so we'll need the rest of the riddle to whittle the field down to one.
“Only in reverse gear” means that she is by no means a progressive, i.e. she is a staunch conservative. This rules out, in particular, Hillary Clinton and Ségolène Royal. As for Sarah Palin, she fits the clues like a glove. She was a basketball point guard, which is a clever double meaning for the second line — the point guard passes the ball (fires the cannon) to other players, and decides which player to pass it to based on tactical considerations (hence acting as a wheel on which the ball turns).
In the final line, “terrorist” means not one who is directly violent, but one who supports a policy of scaremongering, as was the case in the US following 9-11. “How to prove it?” Her opponents were unsuccessful in demonstrating to the American public that her policies were overly strong, which is why she got elected.
The injunction to “pray” and “find the word” in the title alludes to her being Christian, which is a religion of the Word.
The “abstract nonsense” hint refers to category theory. Why point non-mathematicians at category theory? They'll have no idea what it means. “Category theory” here is thus not about the algebraic concept, but rather concerns the everyday meaning of the word “category” — the puzzle looks like math, but that's only for the surface reading, and the answer lies in another category.
I do remain puzzled by the question calling for a word rather than a name. Could this be a nickname? I can't find one that matches the clues.