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 …

We study the Yoneda lemma for arbitrary simplicial spaces. We do that by introducing left
fibrations of simplicial spaces and studying their associated model structure, the covariant …

DOI: https://doi. org/10.1090/noti2692 this graph is reflexive, with the constant path refl𝑥 at
each point 𝑥∈ 𝑋 defining a distinguished endoarrow. Can this reflexive directed graph be …

We give structural results about bifibrations of (internal)(∞, 1)-categories with internal sums.
This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with …

Within the framework of Riehl–Shulman's synthetic (∞, 1)-category theory, we present a
theory of two-sided cartesian fibrations. Central results are several characterizations of the …

We show that the extension types occurring in Riehl--Shulman's work on synthetic $(\infty, 1)
$-categories can be interpreted in the intended semantics in a way so that they are strictly …

We develop a number of basic concepts in the theory of categories internal to an $\infty $-
topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal …

arXiv:2402.00331v1 [math.CT] 1 Feb 2024 Page 1 arXiv:2402.00331v1 [math.CT] 1 Feb 2024
Smooth and Proper Maps Mathieu Anel ∗ Jonathan Weinberger † January 31, 2024 To André …

We provide a generalized treatment of (co) cartesian arrows, fibrations, and functors.
Compared to the classical conditions, the endpoint inclusions get replaced by arbitrary …

Tope logic comprises the top two layers of Riehl and Shulman's type theory for synthetic∞-
categories [3](we will refer to this type theory as RSTT 1). Reasoning in higher categories …