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[ספר][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 …
[ספר][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 …
Nonabelian algebraic topology
This talk gave a sketch of the contents and background to a book with the titleNonabelian
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …
On the unicity of the theory of higher categories
We axiomatise the theory of $(\infty, n) $-categories. We prove that the space of theories of
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …
[ספר][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 …
[ספר][B] The homotopy theory of (∞, 1)-categories
JE Bergner - 2018 - books.google.com
The notion of an (∞, 1)-category has become widely used in homotopy theory, category
theory, and in a number of applications. There are many different approaches to this …
theory, and in a number of applications. There are many different approaches to this …
[HTML][HTML] The 2-category theory of quasi-categories
In this paper we re-develop the foundations of the category theory of quasi-categories (also
called∞-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi …
called∞-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi …
Comparison of models for (∞, n)–categories, I
While many different models for (∞, 1)–categories are currently being used, it is known that
they are Quillen equivalent to one another. Several higher-order analogues of them are …
they are Quillen equivalent to one another. Several higher-order analogues of them are …
On the unicity of the homotopy theory of higher categories
We axiomatise the theory of $(\infty, n) $-categories. We prove that the space of theories of
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …
Gray tensor products and lax functors of (∞, 2)-categories
We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is
associative and forms a left Quillen bifunctor with respect to the bicategorical model category …
associative and forms a left Quillen bifunctor with respect to the bicategorical model category …