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**Higher algebra ** written by ** NA **
This is an other great mathematics book cover the following topics.

Foundations, Stability, The Homotopy Category of a Stable 8-Category, Closure Properties of Stable 8-Categories, Exact Functors, Stable 8-Categories and Homological Algebra, t-Structures on Stable 8-Categories, Filtered Objects and Spectral Sequences, The Dold-Kan Correspondence, The 8-Categorical Dold-Kan Correspondence, Homological Algebra and Derived Categories, Nerves of Differential Graded Categories, Derived 8-Categories, The Universal Property of D-(A), Inverting Quasi-Isomorphisms, Grothendieck Abelian Categories, Spectra and Stabilization, The Brown Representability Theorem, Spectrum Objects, The 8-Category of Spectra, Presentable Stable 8-Categories

Foundations, From Colored Operads to 8-Operads, Maps of 8-Operads, Algebra Objects, 8-Preoperads, Constructions of 8-Operads, Subcategories of O-Monoidal 8-Categories, Slicing 8-Operads, Coproducts of 8-Operads, Monoidal Envelopes, Tensor Products of 8-Operads, Day Convolution, Disintegration and Assembly, Unital 8-Operads, Generalized 8-Operads, Approximations to 8-Operads, Disintegration of 8-Operads, Products and Coproducts, Cartesian Symmetric Monoidal Structures, Monoid Objects, CoCartesian Symmetric Monoidal Structures, Wreath Products

Free Algebras, Operadic Colimit Diagrams, Operadic Left Kan Extensions, Construction of Free Algebras, Transitivity of Operadic Left Kan Extensions, Limits and Colimits of Algebras, Unit Objects and Trivial Algebras, Limits of Algebras, Colimits of Algebras, Tensor Products of Commutative Algebras, Modules over 8-Operads, Coherent 8-Operads, A Coherence Criterion, Module Objects, General Features of Module 8-Categories, Algebra Objects of 8-Categories of Modules, Modules over Trivial Algebras, Limits of Modules, Colimits of Modules

Associative Algebras, The Associative 8-Operad, Monoid Objects of 8-Categories, Planar 8-Operads and A8-Algebras, Nonunital An-Algebras and Nonunital An-Monoids, From An-Algebras to An+1-Algebras, The Associahedron, Monoidal Model Categories, Rectification of Associative Algebras, Left and Right Modules, The 8-Operad LM?, Simplicial Models for Algebras and Modules, Limits and Colimits of Modules, Free Modules, Bimodules, The 8-Operad BM?, Bimodules, Left Modules, and Right Modules, Limits, Colimits, and Free Bimodules, The Relative Tensor Product, Multilinear Maps, Tensor Products and the Bar Construction, Associativity of the Tensor Product, Modules over Commutative Algebras, Left and Right Modules over Commutative Algebras, Tensor Products over Commutative Algebras, Change of Algebra, Rectification of Commutative Algebras, Duality, Duality in Monoidal 8-Categories, Duality of Bimodules, Exchanging Right and Left Actions, Smooth and Proper Algebras, Frobenius Algebras, Monads and the Barr-Beck Theorem, Endomorphism 8-Categories, Split Simplicial Objects, The Barr-Beck Theorem, BiCartesian Fibrations, Descent and the Beck-Chevalley Condition, Tensor Products of 8-Categories, Tensor Products of 8-Categories, Smash Products of Spectra, Algebras and their Module Categories, Properties of RModA(C), Behavior of the Functor T

Definitions and Basic Properties, Little Cubes and Configuration Spaces, The Additivity Theorem, Tensor Products of Ek-Modules, Comparison of Tensor Products, Bar Constructions and Koszul Duality, Twisted Arrow 8-Categories, The Bar Construction for Associative Algebras, Iterated Bar Constructions, Reduced Pairings, Koszul Duality for Ek-Algebras, Iterated Loop Spaces, Centers and Centralizers, Centers and Centralizers, The Adjoint Representation, Tensor Products of Free Algebras, Little Cubes and Manifold Topology, Embeddings of Topological Manifolds, Variations on the Little Cubes Operads, Digression: Nonunital Associative Algebras and their Modules, Nonunital Ek-Algebras, Little Cubes in a Manifold, Topological Chiral Homology, The Ran Space Topological Chiral Homology, Properties of Topological Chiral Homology, Factorizable Cosheaves and Ran Integration, Verdier Duality, Nonabelian Poincare Duality

The Calculus of Functors, n-Excisive Functors, The Taylor Tower, Functors of Many Variables, Symmetric Functors, Functors from Spaces to Spectra, Norm Maps, Differentiation, Derivatives of Functors, Stabilization of Differentiable Fibrations, Differentials of Functors, Generalized Smash Products, Stabilization of 8-Operads, Uniqueness of Stabilizations, The Chain Rule, Cartesian Structures, Composition of Correspondences, Derivatives of the Identity Functor, Differentiation and Reduction, Consequences of Theorem, The Dual Chain Rule

Structured Ring Spectra, E1-Rings and Their Modules, Recognition Principles, Change of Ring, Algebras over Commutative Rings, Properties of Rings and Modules, Free Resolutions and Spectral Sequences, Flat and Projective Modules, Localizations and Ore Conditions, Finiteness Properties of Rings and Modules, The Cotangent Complex Formalism, Stable Envelopes and Tangent Bundles, Relative Adjunctions, The Relative Cotangent Complex, Tangent Bundles to 8-Categories of Algebras, The Cotangent Complex of an Ek-Algebra, The Tangent Correspondence, Deformation Theory, Square-Zero Extensions, Deformation Theory of E8-Algebras, Connectivity and Finiteness of the Cotangent Complex, EtaleMorphisms, EtaleMorphisms of ´ E1-Rings, The Nonconnective Case , Cocentric Morphisms, EtaleMorphisms of ´ Ek-Rings

Locally Constant Sheaves, Homotopy Invariance, The Seifert-van Kampen Theorem, Singular Shape, Constructible Sheaves, 8-Categories of Exit Paths, A Seifert-van Kampen Theorem for Exit Paths, Digression: Recollement, Exit Paths and Constructible Sheaves

P-Anodyne Morphisms, The Model Structure on (Set+/ P, Flat Inner Fibrations, Functoriality

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