Abstract
Equivalence of sketches S and T means the equivalence of their categories ModS and ModT of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category ModT. For general sketches, we show that an analogous result holds provided that ModT is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is ∏(ModT), the free product completion of ModT.
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Adámek, J., Borceux, F. Morita Equivalence of Sketches. Applied Categorical Structures 8, 503–517 (2000). https://doi.org/10.1023/A:1008735511095
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DOI: https://doi.org/10.1023/A:1008735511095