Benno van den Berg
Abstract
We compare three categorical models of type theory with extensional constructs: setoids over extensional type theory; setoids over intensional type theory and a certain free exact category (the free ‘ΠW-pretopos’). By studying the amount of choice available in these categories, we are able show that they are distinct.
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We compare three categorical models of type theory with extensional constructs: setoids over extensional type theory; setoids over intensional type theory and a certain free exact category (the free ‘ΠW-pretopos’). By studying the amount of choice available in these categories, we are able show that they are distinct.
Key concepts: Extensional definition, Type theory, Type (biology), Categorical variable, Extensionality, Mathematics, Computer science, Discrete mathematics