@MISC{Schröder02classifyingcategories, author = {Lutz Schröder}, title = {Classifying Categories for Partial Equational Logic}, year = {2002} }

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Abstract

Along the lines of classical categorical type theory for total functions, we establish equivalence results between certain classes of partial equational theories on the one hand and corresponding classes of categories on the other hand, staying close to standard categorical notions.