Kant states in the Critique of Pure Reason (English translation) that
Thus the entire armament of reason, in the undertaking that one can call pure philosophy, is in fact directed only at the three problems that have been mentioned. These themselves, however, have in turn their more remote aim, namely, what is to be done if the will is free, if there is a God, and if there is a future world. Now since these concern our conduct in relation to the highest end, the ultimate aim of nature which provides for us wisely in the disposition of reason is properly directed only to what is moral. (A801)
The Critique of Pure Reason translation used in the wikipedia article on the matter is
All the preparations of reason, therefore, in what may be called pure philosophy, are in reality directed to those three problems only [God, the soul, and freedom]. However, these three elements in themselves still hold independent, proportional, objective weight individually. Moreover, in a collective relational context; namely, to know what ought to be done: if the will is free, if there is a God, and if there is a future world. As this concerns our actions with reference to the highest aims of life, we see that the ultimate intention of nature in her wise provision was really, in the constitution of our reason, directed to moral interests only. (A801)
I happen to find the first translation clearer (it comes from the pdf I am reading), but Wikipedia derives its analysis from the second one.
Kant had before established that it is impossible to either prove or disprove the existence of God. Wikipedia interprets this passage as arguing that thus, the next step in determining whether to accept the existence of God is to see whether it is in our interest to believe in God.
Now, Kant had previously in his epistomological expositions established categories of reason, which we humans impose onto the world. He dealt with Hume's skepticism by arguing that when we humans observe the world, we impose the category of causality (under a relation of ideas in his table of judgement) onto the world, just like a person with red glasses imposed the color red onto the world (courtesy of Sophie's world).
In both instances, Kant defends the attacks on the belief of God and of casuality, showing that both cannot be rationally proven. But then, he defends bothc casuality and the belief in God through two different mechanisms; for casuality he places it as a category of understanding, while with God he argues that it is in the interest of man to believe in God.
Now, my question is whether these mechanisms are related? Is the defense of the belief of god related to the concept of categories of understanding, or are these two completely different ideas within Kant's philosophical framework? If they are related, how? (Any relevant passages from an internet source or Kant's Critique of Pure Reason would be appreciated.)