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Yes in general. See Adámek and Rosicky, Locally Presentable and Accessible Categories Cambridge University Press, Cambridge, (1994). T. 3.12 p. 143. Of course "in general" I mean: every "algebraic theory" (many sorted) Set models. For topological algebraic structures, (like profinite groups) this equivalence isn't true for the Yiftach Barnea example |
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Yes in general. See Adámek and Rosicky, Locally Presentable and Accessible Categories Cambridge University Press, Cambridge, (1994). T. 3.12 p. 143. |
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