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Higher Algebra II (PDF 950P)
This note covers the following topics: Disintegration and Assembly, Associative Algebras and Their Modules, Algebras and Modules over alpha operads, Little Cubes and Factorizable Sheaves, Algebraic Structures on alpha Categories, Algebra in the Stable Homotopy Category.
Author(s): Jacob Lurie
950 Pages 
An Introduction to Higher Categorical Algebra
This note covers introduction, Category theory, Ring theory, Module theory and deformation theory.
Author(s): David Gepner
69 Pages
This note explains the following topics: Group Theory, Sylow’s Theorem, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products.
Author(s): David Surowski
194 Pages
Homotopical and Higher Algebra
This note covers the following topics: The symmetric monoidal category nCob and nTFTs, Duality in monoidal categories, Presentation of 1Cob by generators and relations, 2TFTs and Frobenius algebra, Extending down TFTs, Bicategories, Symmetric monoidal bicategories, Symmetric monoidal structures on higher categories.
Author(s): ETH Zurich University
NA Pages
This note covers the following topics: Disintegration and Assembly, Associative Algebras and Their Modules, Algebras and Modules over alpha operads, Little Cubes and Factorizable Sheaves, Algebraic Structures on alpha Categories, Algebra in the Stable Homotopy Category.
Author(s): Jacob Lurie
950 Pages
Tools From Higher Algebra (PDF 42P)
This note covers the following topics: group theory and graphs with large girth, expanders and superconcentrators, character sums and pseudo-random graphs, real varieties and sign patterns of polynomials, The Chevalley-Warning theorem, Abelian groups and regular graphs, hyperbolic geometry and triangulations of polytopes and polygons, the Erdos-Mozer conjecture and the hard Lefschetz theorem.
Author(s): Noga Alon
42 Pages
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Author(s): NA
NA Pages