" The book is extremely pleasant to read, with masterfully crafted exercises and examples
that create a beautiful and unique thread of presentation leading the reader safely into the …

This book provides an introduction to modern homotopy theory through the lens of higher
categories after Joyal and Lurie, giving access to methods used at the forefront of research …

Our goal in this paper is to prove an equivalence between the model categorical approach
to pro-categories, as studied by Isaksen, Schlank and the first author, and the∞–categorical …

We combine the language of monoids with the language of preorders so as to refine some
fundamental aspects of the classical theory of factorization and prove an abstract …

Any scheme has its associated little and big Zariski toposes. These toposes support an
internal mathematical language which closely resembles the usual formal language of …

This work concerns the theoretical foundations of persistence-based topological data
analysis. We develop theory of topological inference in the multidimensional persistence …

'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic
geometry (see eg arXiv: 1106.4882), as the geometric structure on moduli spaces of $ J …

Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die
strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren …

The aim of this book is to introduce the basic aspects of the theory of∞-categories: a
homotopy theoretic variation on Category Theory, designed to implement the methods of …

The rules governing the essentially algebraic notion of a category with families have been
observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a …