General overview about Recursion (free online texts)

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I'm looking for free online texts about recursion.

What I'm looking for formal definitions* of "all" (most of) the different types of recursion and from different points of views like Category theory too .

For example I did read a text where the author talks about the "successor algebra" $(\Bbb N,S)$ (he calls it in this way) and how there exist an unique homomorphism $f: \Bbb N \rightarrow X$ between the "successor algebra" and another structure $(X,e)$ such that $f \circ S = e \circ f$ and that $f$ can be easily identified with a function defined recursively on the natural numbers by $S$ and $e$

so what I need is:

A general overview of everything that concerns the recursion in a synthetic way but NOT FROM THE POINT OF VIEW OF COMPUTER.


note: I'm also interested if there is some general discussion of the process of recursion as a kind function $R$ that map functions, for example $f$ and $S$ to another function $F=R(f,S)$ that is "defined recursively"


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