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Yoneda Lemma for -Simplicial Spaces
Nima Rasekh
For a small category we define fibrations of simplicial presheaves on the category , which we call localized -left fibration. We show…
Univalence in Higher Category Theory
Nima Rasekh
Univalence was first defined in the setting of homotopy type theory by Voevodsky, who also (along with Kapulkin and Lumsdaine) adapted it to a model categorical setting, which was…
Cartesian Fibrations of Complete Segal Spaces
Nima Rasekh
Cartesian fibrations were originally defined by Lurie in the context of quasi-categories and are commonly used in -category theory to study presheaves valued in $(\inft…
Quasi-Categories vs. Segal Spaces: Cartesian Edition
Nima Rasekh
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces,…
Filter Quotients and Non-Presentable -Toposes
Nima Rasekh
We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter q…
An Elementary Approach to Truncations
Nima Rasekh
We study truncated objects using elementary methods. Concretely, we use universes and the resulting natural number object to define internal truncation levels and prove they behave…