# Homotopy Theory of Higher Categories: From Segal Categories by Carlos Simpson

By Carlos Simpson

The learn of upper different types is attracting starting to be curiosity for its many functions in topology, algebraic geometry, mathematical physics and class concept. during this hugely readable e-book, Carlos Simpson develops a whole set of homotopical algebra recommendations and proposes a operating thought of upper different types. beginning with a cohesive evaluate of the various assorted ways presently utilized by researchers, the writer proceeds with an in depth exposition of 1 of the main universal options: the development of a Cartesian Quillen version constitution for larger different types. The totally iterative development applies to enrichment over any Cartesian version classification, and yields version different types for weakly associative n-categories and Segal n-categories. A corollary is the development of upper functor different types which are compatible jointly to shape the (n+1)-category of n-categories. The method makes use of Tamsamani's definition in response to Segal's principles, iterated as in Pelissier's thesis utilizing sleek concepts because of Barwick, Bergner, Lurie and others.

Read Online or Download Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond (New Mathematical Monographs) PDF

Similar geometry & topology books

Finsler Geometry: An Approach via Randers Spaces

"Finsler Geometry: An procedure through Randers areas" solely bargains with a distinct type of Finsler metrics -- Randers metrics, that are outlined because the sum of a Riemannian metric and a 1-form. Randers metrics derive from the learn on common Relativity thought and feature been utilized in lots of parts of the normal sciences.

Mathematical Concepts

The most goal of this publication is to explain and strengthen the conceptual, structural and summary considering arithmetic. particular mathematical constructions are used to demonstrate the conceptual strategy; delivering a deeper perception into mutual relationships and summary universal positive factors. those principles are rigorously encouraged, defined and illustrated through examples in order that a few of the extra technical proofs may be passed over.

Modern General Topology (Bibliotheca Mathematica)

Bibliotheca Mathematica: a chain of Monographs on natural and utilized arithmetic, quantity VII: smooth basic Topology specializes in the approaches, operations, ideas, and techniques hired in natural and utilized arithmetic, together with areas, cardinal and ordinal numbers, and mappings. The e-book first elaborates on set, cardinal and ordinal numbers, uncomplicated innovations in topological areas, and numerous topological areas.

Fractal Functions, Fractal Surfaces, and Wavelets

Fractal capabilities, Fractal Surfaces, and Wavelets, moment version, is the 1st systematic exposition of the speculation of neighborhood iterated functionality platforms, neighborhood fractal capabilities and fractal surfaces, and their connections to wavelets and wavelet units. The ebook is predicated on Massopust’s paintings on and contributions to the idea of fractal interpolation, and the writer makes use of a couple of tools—including research, topology, algebra, and likelihood theory—to introduce readers to this interesting topic.

Additional resources for Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond (New Mathematical Monographs)

Example text