We develop new techniques for constructing model structures from a given class of
cofibrations, together with a class of fibrant objects and a choice of weak equivalences …

We show that any pasting diagram in any $(\infty, 2) $-category has a homotopically unique
composite. This is achieved by showing that the free 2-category generated by a pasting …

We construct a nerve from double categories into double $(\infty, 1) $-categories and show
that it gives a right Quillen and homotopically fully faithful functor between the model …

We provide an (∞, n)-categorical version of the straightening-unstraightening construction,
asserting an equivalence between the (∞, n)-category of double (∞, n− 1)-right fibrations …

What is an equivalence in a higher category? - Ozornova - 2024 - Bulletin of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …

We provide an $(\infty, n) $-categorical version of the straightening-unstraightening
construction, asserting an equivalence between the $(\infty, n) $-category of double $(\infty …

We define limits for diagrams valued in an $(\infty, n) $-category. As a model of $(\infty, n) $-
categories, we use complete Segal objects in $(\infty, n-1) $-categories. We show that this …

The language of higher categories provides a way to describe many phenomena in areas of
mathematics as diverse as topology, algebra, geometry, and mathematical physics. In a …

We study several flavors of homotopy coherent nerves for enriched categories, in the form of
right Quillen functors valued in simplicial objects. In particular, we extract explicit models for …

An explicit comparison between 2–complicial sets and 2–spaces Page 1 A Tg Algebraic &
Geometric Topology msp Volume 24 (2024) An explicit comparison between 2–complicial …