1. S. Awodey & M. A. Warren (2013). Martin-Löf Complexes. Annals of Pure and Applied Logic 164 (10):928-956.
    In this paper we define Martin-L¨of complexes to be algebras for monads on the category of (reflexive) globular sets which freely add cells in accordance with the rules of intensional Martin-L¨of type theory. We then study the resulting categories of algebras for several theories. Our principal result is that there exists a cofibrantly generated Quillen model structure on the category of 1-truncated Martin-L¨of complexes and that this category is Quillen equivalent to the category of groupoids. In particular, 1-truncated Martin-L¨of complexes (...)
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  2. S. Awodey, N. Gambino & M. A. Warren (2009). Lawvere-Tierney Sheaves in Algebraic Set Theory. Journal of Symbolic Logic 74 (3):861 - 890.
    We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.
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  3. M. A. Warren (1997). On the Legal and Moral Status of Abortion. In Hugh LaFollette - (ed.), Ethics in Practice. Basil Blackwell.
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