https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
Emily Riehl:
"The author is told with distressing regularity that 'there are no theorems in category theory' ...
Sadly, the majority of the theorems that are personal favorites of the author were excluded because their significance is more difficult to explain."
(long list of theorems)
https://math.jhu.edu/~eriehl/161/context.pdf
https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
Emily Riehl:
"The author is told with distressing regularity that 'there are no theorems in category theory' ...
Sadly, the majority of the theorems that are personal favorites of the author were excluded because their significance is more difficult to explain."
(long list of theorems)
https://math.jhu.edu/~eriehl/161/context.pdf