1. Steve Awodey & Michael A. Warren, Homotopy Theoretic Models of Identity Types.
    Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  2. Pieter Hofstra & Michael A. Warren (2013). Combinatorial Realizability Models of Type Theory. Annals of Pure and Applied Logic 164 (10):957-988.
    We introduce a new model construction for Martin-Löf intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines, by gluing along the functor from the category of contexts to the category of groupoids, the syntactic model with a notion of realizability. As our main application, we use the model to analyse the syntactic groupoid associated to the type theory generated by a graph G, showing that it has the same homotopy type (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  3. Michael A. Warren (2007). Coalgebras in a Category of Classes. Annals of Pure and Applied Logic 146 (1):60-71.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation