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Categories with Dependence and Semantics of Dependent Types
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math.CTcs.LO
keywords
categoriescartesiancloseddependencedependentsemanticsstrictcalled
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The present paper gives a generalization of cartesian closed categories, called cartesian closed categories with dependence, whose strict version induces categories with families that support 1-, Sigma- and Pi-types in the strict sense. Consequently, we have obtained a new semantics of dependent type theories that is both categorical and true-to-syntax.
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