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In the book "Topos Theory" of Peter Johnstone (Topos Theory, LMS Monographs no. 10. Academic, 1977) can read at 0page 41 in Chapter 2:

"For a detaled account of internal categories from a 2-Categorical point of view, the reader is Referred to the monumental work of JW Gray [168]"

The work of J.W. Gray has to be very important and significant (in those years was one of the great masters of the theory of categories) as well known and whose output is only the first part in Formal Category Theory: Adjointness for 2-Categories. Series: Lecture Notes in Mathematics, Vol 391.

Does anyone have news of such notes of J.W. Gray? Of course I would like read these.

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For everyone else: reference [168] from Johnstone is "Formal category theory II, To appear". @Buschi My advice is to look at work by Street, Kelly and Lack. I don't have proper references at the moment, I'm afraid. 'Tis late and I've got to get up early for prezzies :) At least look at Fibrations in bicategories by Street: – David Roberts Dec 24 '10 at 11:20
Why don't you write Gray? His information is at – Todd Trimble Dec 24 '10 at 11:59

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