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doi:10.1016/S0168-0072(00)00012-9 
Copyright © 2000 Elsevier Science B.V. All rights reserved.
Wellfounded trees in categories
Received 1 December 1998;
revised 31 August 1999.
Available online 5 July 2001.
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Abstract
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.
Author Keywords: Initial algebras; Locally cartesian closed categories; Pretoposes; Artin gluing; Sheaves; Wellfounded trees; Martin-Löf type theory
Mathematical subject codes: primary: 03B15; 03G30; 18A15; 18B25; 18C15; 18F20; secondary: 18C50; 68N18
