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In this paper, we identify a general fibrational condition for the IA-FC coincidence, namely in the fiber over an initial algebra in the base category. ... Practical benefits of our categorical theory are exemplified by new "upside-down" witness notions for three verification problems: probabilistic liveness, and acceptance and model-checking with respect ... In Marcel Vinícius Medeiros Oliveira and Jim Woodcock, editors, Formal Methods: Foundations and Applications, 12th Brazilian Symposium on Formal Methods, SBMF 2009, Gramado, Brazil, August 19-21, 2009 ...arXiv:2105.04817v2 fatcat:ghexq4ttgvdbfga3yfiuliat6i