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Annals of Pure and Applied Logic, Vol. 104, No. 1-3. (July 2000), pp. 189-218, doi:10.1016/s0168-0072(00)00012-9 Key: citeulike:11556771
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In this paper we present and study a categorical formulation of the W-types of Martin-Löf. These are essentially free term algebras where the operations may have finite or infinite arity. It is shown that W-types are preserved under the construction of sheaves and Artin gluing. In the proofs we avoid using impredicative or nonconstructive principles.
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