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Also, a catalyst only speeds up a reaction. It does not change the thermodynamics of a reaction. An irreversible reaction with the addition of a catalyst is still irreversible.

catalysts are not consumed in the reaction, by definition

Yao, B., Xiao, T., Makgae, O.A. et al. "Transforming carbon dioxide into jet fuel using an organic combustion-synthesized Fe-Mn-K catalyst." Nat Commun 11, 6395 (2020). https://doi.org/10.1038/s41467-020-20214-z