4-4 point low approach one-space high pincer
This pincer discourages tenuki.
There are some interesting variations when Black tries to steal White's base.
next is normal. Also played are the 3-3 invasion at a, the attachments at b and c, and the double kakaris at d and e.
This is joseki, but White has no reason to be dissatisfied; compared to the catenaccio joseki White has better aji.
is often played now immediately after the joseki. Later Black can aim at making a big ko with and .
Charles See ko preparation for some examples of this.
Therefore is played in an attempt to force White. If White simply answers at a, Black can go back happily to b.
White more often plays the atekomi at here to gain some shape. Black simply connects at , and White takes the corner with . Black's payoff comes with , when White can answer at a as well as the safe b.
Black can cut with but has to return to in gote; so lives in the corner, and a fight has broken out in the centre. Black usually plays . White has some bad shape but also has chance to capture , since Black's forcing moves at a and b to connect it cause shortage of liberties.
White won't actually play where you suggested but there, thus cutting black. Continuation at a for black. Leviathan