Learn Turkish: Dün sabahladığı için daha geç uyanmış olmalı. - Because he stayed up all night yesterday, he must have woken up later.

Uyanmalı means "he must wake up" (expressing a requirement or obligation for the present/future). To make a logical deduction about the past ("he must have done it"), we put the evidential past ending -mış on the main verb, followed by olmalı. We use -mış rather than -dı because we are making an assumption about something we didn't directly witness.

What is the root of the word sabahladığı?

It comes from the noun sabah (morning). By adding the suffix -la, it becomes the verb sabahlamak, which means "to stay up until morning" or "to pull an all-nighter".

Why does the sentence use sabahladığı için instead of just using the standard past tense, like sabahladı için?

To say "because [someone] did [something]" in Turkish, you can't simply put için after a regular conjugated verb. You have to use a participle structure: the verb takes the -dık suffix (which softens to -dığ) plus a possessive ending (-ı for "his/her"). Literally, sabahladığı için translates to "for his staying up all night".

Could I use sonra instead of daha geç to mean "later" in this sentence?