MoL-2016-13: Frumin, Daniil (2016) Weak Factorisation Systems in the Effective Topos. [Report]
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Abstract
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 |
| URI: | https://eprints.illc.uva.nl/id/eprint/985 |
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