On separation axioms in terms of lifting properties:
Misha Gavrilovich, Point set topology as diagram chasing computations, The De Morgan Gazette. 2014. Vol. 5. No. 4. P. 23-32. (arXiv:1408.6710, pdf)
Misha Gavrilovich, The unreasonable power of the lifting property in elementary mathematics, 2017 (arXiv:1707.06615, pdf)
Misha Gavrilovich, Konstantin Pimenov: A naive diagram chasing approach to formalisation of tame topology [arXiv:1807.06986]
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