Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan
complexes. But at a much simpler level, it allows one to describe sets with operations …

This work investigates the homotopy theory of globular models for higher categorical
structures. In particular, we focus on weak∞-groupoids, but most of the constructions can be …

In [Joyal] where the category Θ is first defined it is noted that the dimensional shift on Θ
suggests an elegant presentation of the unreduced suspension on cellular sets. In this note …

The goal of this paper is to address the problem of building a path object for the category of
Grothendieck (weak) $\infty $-groupoids. This is the missing piece for a proof of …

The main goal of this thesis is to develop the integration theory of curved homotopy Lie
algebras. In the first chapter, we develop the operadic calculus needed: we encode non …

En un sens la logique catégorique débute avec les travaux de W. Lawvere en 1964 ([33])
qui donnent une axiomatisation de la catégorie des ensembles (appelée ETCS pour …

Cylindrical Model Structures Page 1 Cylindrical Model Structures Richard Williamson arXiv:1304.0867v2
[math.CT] 23 Apr 2016 Page 2 Dedicated to Kari Chard Page 3 Abstract We build a model …

We study abelian group objects in $\omega $-categories and discuss the well-known Dold-
Kan correspondence from the perspective of $\omega $-categories as a model for strict …

Categorical Model Structures Page 1 Doctor of Philosophy Thesis Categorical Model Structures
Richard Williamson University College University of Oxford Trinity 2011 Page 2 Dedicated to …