Trees, Prisms and a Quillen Model Structure on Prismatic Sets

Title: Trees, Prisms and a Quillen Model Structure on Prismatic Sets
Identifier: d_2009_2013:1a59d88ff745:11969
identifier: 12639
Creator: Thrall, Louis,
Contributor: Martin Bendersky
Date: 2013
Language: English
Publisher: City University of New York.
Subject: Mathematics | Applied mathematics | category theory | homotopy theory | presheaf category | test category
Abstract: We define a category which we call the category of prisms, P . This category interpolates between the simplex category, &utri; and the box category &square;. 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 P 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 P is a test category automatically giving a Quillen model structure on the presheaves on P .
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics