Skip to search formSkip to main contentSkip to account menu
Synthetic fibered (∞, 1)-category theory
TLDR
This work develops a Yoneda Lemma for cocartesian fibrations in the setting of the synthetic (∞, 1)-category theory developed in simplicial type theory introduced by Riehl and Shulman.
Synthetic fibered (∞, 1)-category theory
TLDR
This work develops a Yoneda Lemma for cocartesian fibrations in the setting of the synthetic (∞, 1)-category theory developed in simplicial type theory introduced by Riehl and Shulman.
View PDF on arXiv
HIGHER ELLIPTIC GENERA
We show that elliptic classes introduced in [7] for spaces with infinite fundamental groups yield Novikov’s type higher elliptic genera which are invariants of Kequivalence. This include, as a…
A Synthetic Perspective on (∞, 1)-Category Theory: Fibrational and Semantic Aspects
Two-sided cartesian fibrations of synthetic (∞, 1)-categories
View via Publisher
Strict stability of extension types
. We show that the extension types occurring in Riehl–Shulman’s work on synthetic ( ∞ , 1)-categories can be interpreted in the intended seman- tics in a way so that they are strictly stable under…
View PDF on arXiv
Synthetic Tait Computability for Simplicial Type Theory
Riehl and Shulman [13] introduced a simplicial extension of (homotopy) type theory to reason synthetically about (∞, 1)-categories. Indeed, the semantics of this theory matches up with established…
Review of R. M. Sainsbury, Paradoxes, second edition
Simplicial sets inside cubical sets
As observed by various people recently the topos $\mathbf{sSet}$ of simplicial sets appears as essential subtopos of a topos $\mathbf{cSet}$ of cubical sets, namely presheaves over the category…
View PDF on arXiv
A Synthetic Perspective on $(\infty,1)$-Category Theory: Fibrational and Semantic Aspects
Reasoning about weak higher categorical structures constitutes a challenging task, even to the experts. One principal reason is that the language of set theory is not invariant under the weaker…
View PDF on arXiv
...
...
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy, Terms of Service, and Dataset License