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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 …
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 …
particular focus on examples. Part I discusses two competing perspectives by which one …
[كتاب][B] Elements of?-Category Theory
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 …
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …
All -toposes have strict univalent universes
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 …
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 …
symmetries of manifolds. Several important equivariant phenomena occur not just for a …
Univalence for inverse diagrams and homotopy canonicity
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 …
generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy …
A necessary and sufficient condition for induced model structures
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 …
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 …
topology, algebraic geometry, mathematical physics and category theory. In this highly …
The theory and practice of Reedy categories
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 …
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 …
simplicial and dendroidal sets and spaces. These are essential for the study of categories …