We define a category which we call the category of prisms, [special characters omitted]. This category interpolates between the simplex category, ▵ and the box category □. The way in which we interpolate these two categories is considering categories with a tensor functor and a cone functor. It turns out that the objects of the category [special characters omitted] are in one to one correspondence with planer rooted trees. Furthermore the morphisms of this category may be defined as certain combinatorial decorations on certain trees. We then show that that the category [special characters omitted] is a test category automatically giving a Quillen model structure on the presheaves on [special characters omitted].
|Commitee:||Bendersky, Martin, Thompson, Robert, Yanofsky, Noson|
|School:||City University of New York|
|School Location:||United States -- New York|
|Source:||DAI-B 75/02(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Category theory, Homotopy theory, Presheaf category, Prismatic sets, Test category|
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