Homotopy of operads and Grothendieck-Teichmuller groups

B Fresse - 2017‏ - books.google.com
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as
defined by Drinfeld in quantum group theory, has a topological interpretation as a group of …

[كتاب][B] Categorical homotopy theory

E Riehl - 2014‏ - books.google.com
This book develops abstract homotopy theory from the categorical perspective with a
particular focus on examples. Part I discusses two competing perspectives by which one …

[كتاب][B] Elements of?-Category Theory

E Riehl, D Verity - 2022‏ - books.google.com
The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

All -toposes have strict univalent universes

M Shulman - arxiv preprint arxiv:1904.07004, 2019‏ - arxiv.org
We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

[كتاب][B] Global homotopy theory

S Schwede - 2018‏ - books.google.com
Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

Univalence for inverse diagrams and homotopy canonicity

M Shulman - Mathematical Structures in Computer Science, 2015‏ - cambridge.org
We describe a homotopical version of the relational and gluing models of type theory, and
generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy …

A necessary and sufficient condition for induced model structures

K Hess, M Kȩdziorek, E Riehl, B Shipley - Journal of Topology, 2017‏ - Wiley Online Library
A common technique for producing a new model category structure is to lift the fibrations and
weak equivalences of an existing model structure along a right adjoint. Formally dual but …

[كتاب][B] Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond

C Simpson - 2011‏ - books.google.com
The study of higher categories is attracting growing interest for its many applications in
topology, algebraic geometry, mathematical physics and category theory. In this highly …

The theory and practice of Reedy categories

E Riehl, D Verity - arxiv preprint arxiv:1304.6871, 2013‏ - arxiv.org
The goal of this paper is to demystify the role played by the Reedy category axioms in
homotopy theory. With no assumed prerequisites beyond a healthy appetite for category …

[كتاب][B] Simplicial and dendroidal homotopy theory

G Heuts, I Moerdijk - 2022‏ - library.oapen.org
This open access book offers a self-contained introduction to the homotopy theory of
simplicial and dendroidal sets and spaces. These are essential for the study of categories …