Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Riehl, Emily"'
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber cate
Externí odkaz:
http://arxiv.org/abs/2406.18497
Formalized $1$-category theory forms a core component of various libraries of mathematical proofs. However, more sophisticated results in fields from algebraic topology to theoretical physics, where objects have "higher structure," rely on infinite-d
Externí odkaz:
http://arxiv.org/abs/2309.08340
Autor:
Riehl, Emily
The extension of ordinary category theory to $\infty$-categories at the start of the 21st century was a spectacular achievement pioneered by Joyal and Lurie with contributions from many others. Unfortunately, the technical arguments required to solve
Externí odkaz:
http://arxiv.org/abs/2302.07855
Autor:
Riehl, Emily
Publikováno v:
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Feb 2024, Pages 461-879
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article, written as lecture notes to accompany a 3-part mini course delivered
Externí odkaz:
http://arxiv.org/abs/2212.06937
Autor:
Hazratpour, Sina, Riehl, Emily
Publikováno v:
Math. Struct. Comp. Sci. 34 (2024) 258-280
Consider a locally cartesian closed category with an object I and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential with the ge
Externí odkaz:
http://arxiv.org/abs/2210.00078
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 2171-2183
The inclusion of 1-categories into $(\infty,1)$-categories fails to preserve colimits in general, and pushouts in particular. In this note, we observe that if one functor in a span of categories belongs to a certain previously-identified class of fun
Externí odkaz:
http://arxiv.org/abs/2205.02353
Autor:
Riehl, Emily, Wattal, Mira
An $\infty$-cosmos is a setting in which to develop the formal category theory of $(\infty,1)$-categories. In this paper, we explore a few atypical examples of $\infty$-cosmoi whose objects are 2-categories or bicategories rather than $(\infty,1)$-ca
Externí odkaz:
http://arxiv.org/abs/2108.11786