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- W3203176006 abstract "We present a construction of W-types in the setoid model of extensional Martin-Lof type theory using dependent W-types in the underlying intensional theory. More precisely, we prove that the internal category of setoids has initial algebras for polynomial endofunctors. In particular, we characterise the setoid of algebra morphisms from the initial algebra to a given algebra as a setoid on a dependent W-type. We conclude by discussing the case of free setoids. We work in a fully intensional theory and, in fact, we assume identity types only when discussing free setoids. By using dependent W-types we can also avoid elimination into a type universe. The results have been verified in Coq and a formalisation is available on the author's GitHub page." @default.
- W3203176006 created "2021-10-11" @default.
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- W3203176006 date "2021-09-24" @default.
- W3203176006 modified "2023-10-18" @default.
- W3203176006 title "W-types in setoids" @default.
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- W3203176006 doi "https://doi.org/10.46298/lmcs-17(3:28)2021" @default.
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