Which case is "I am a professor" with identity view? According to the Yamaka Sutta quoted below, a run-of-the-mill person thinks one of the following:


the form to be the self
the self as possessing form
the form as in the self
the self as in form


And the same applies to the other aggregates.

If someone says with identity view, that "I am a professor", "I am an American", "I am successful" etc., what would this case be?

Is "professor" a mental fabrication? So, "I am a professor" (with identity view) would be the case of assuming a mental fabrication to be the self?

From the Yamaka Sutta (SN 22.85):


  "In the same way, an uninstructed, run-of-the-mill person — who has no
  regard for noble ones, is not well-versed or disciplined in their
  Dhamma; who has no regard for men of integrity, is not well-versed or
  disciplined in their Dhamma — assumes form (the body) to be the self,
  or the self as possessing form, or form as in the self, or the self as
  in form.
  
  "He assumes feeling to be the self...
  
  "He assumes perception to be the self...
  
  "He assumes (mental) fabrications to be the self...
  
  "He assumes consciousness to be the self, or the self as possessing
  consciousness, or consciousness as in the self, or the self as in
  consciousness.
"I am a professor" is conceit not self view. But if self view arises before conceit as "professor is attā", then the conceit, which arises after that, will become misunderstood conceit.

The explanation

There are 3 clauses in tipiṭaka:


"etaṃ  mama-this is mind"  is thought by taṇhā.
"esohamasmi-I am this"  is thought by māna. &lt;&lt;&lt; this is conceit.
"eso me  attā-this is my attā" is thought by diṭṭhi. &lt;&lt;&lt; only this one is compatible with your quoted identity view,  Yamaka Sutta (SN 22.85).


But there are the complicated arising of taṇhā, māna, and diṭṭhi, because taṇhā must co-arises with only one, diṭṭhi or māna, per mind-moment arising. And  diṭṭhi can't co-arises with māna. So:

2 taṇhā = 1. sotāpanna's taṇhā 2. puthujana's taṇhā.

2 diṭṭhi = 1. sotāpanna's diṭṭhi 2. puthujana's diṭṭhi.

3 māna = 1. we are the same 2. I am better 3. I am worse.


There are sotāpanna's taṇhā and 3 māna of sotāpanna, but there are not diṭṭhi of sotāpanna.
There are 2 taṇhā, 9 māna, and 2 diṭṭhi of puthujana.


Therefore, there are just 3 māna of sotāpanna, but there are 9 māna for puthujana, 6 Diṭṭhi-Before&amp;After(misunderstood) and 3 No-Diṭṭhi-Before&amp;After māna's arising (right understood).


  
  "eso me  attā-this is my attā" is thought by diṭṭhi. &lt;&lt;&lt; only this one is compatible with your quote,  Yamaka Sutta (SN 22.85).
  


There are 20 sakkāya-diṭṭhi which thinking about attā in Yamaka Sutta (SN 22.85).