morphisms-of-computational-structures
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Understand how coalgebra helps in modal logic
Paper: https://eprints.soton.ac.uk/262612/
Modal Logics are Coalgebraic: https://eprints.soton.ac.uk/267144/1/ModalCoalgRev.pdf http://users.cecs.anu.edu.au/~dpattinson/Publications/visions2008.pdf
There is a really good second year PhD report by Henry Story touching on this aspect: https://co-operating.systems/2019/04/01/PhD_second_year_report.pdf