MoL-2016-13: Weak Factorisation Systems in the Effective Topos

MoL-2016-13: Frumin, Daniil (2016) Weak Factorisation Systems in the Effective Topos. [Report]

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In this thesis we present a new model of Martin-Löf type theory with identity types in the effective topos. Using the homotopical approach to type theory, the model is induced from a Quillen model category structure on a full subcategory of the effective topos. To aid the construction we introduce a general method of obtaining model category structures on a full subcategory of an elementary topos, by starting from an interval object I and restricting our attention to fibrant objects, utilizing the notion of fibrancy similar to the one that Cisinksi employed for constructing a model category structure on a Grothendieck topos with an interval object.
We apply this general method to the effective topos Eff . Following Van Oosten we take the interval object to be I = ∇(2), and derive a model structure on the subcategory Eff_f of fibrant objects. This Quillen model category structure gives rise to a model of type theory in which the identity type for a type X is represented by X^I. It follows that the resulting model supports functional extensionality.

Item Type: Report
Report Nr: MoL-2016-13
Series Name: Master of Logic Thesis (MoL) Series
Year: 2016
Uncontrolled Keywords: logic, computation
Subjects: Logic
Date Deposited: 12 Oct 2016 14:39
Last Modified: 12 Oct 2016 14:39

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