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See attached picture from Toposes, Theories, and Triples by Barr and Wells. ehresmannkennison.png
What is the more general version that Ehresmann is said to have proved?
Well I found his papers that Barr and Wells cite! Here and Here but you have to look at the bibliography of Barr and Wells to go to the right page
(Thanks for mentioning this book, it looks interesting!)
You might also want to look at chapter 6 of Kelly’s book on enriched categories.