Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce categorize as KA-tuh-guh-rahyz (/ˈkæɾəɡəˌraɪz/). In "categorize", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, a hallmark of natural-sounding American speech. It comes out as KA·tuh·guh·RAHYZ. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "I use a budgeting app to categorize all of my monthly expenses".
Record yourself saying "categorize" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
The schwa before R disappears — R becomes the vowel of the syllable. This is the 'er' sound without a distinct vowel before it.

Start with your jaw open wide and your tongue resting low and flat. Glide the front of your tongue up toward the roof of your mouth as your jaw closes halfway.
Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "categorize", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the first syllable, not the others. Stretch KA — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.