Alphabeta MathGraded Bimodules and Tensor Functors — Examples
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Cosets, Index and Lagrange's Theorem
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Homomorphisms and the Isomorphism Theorems
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
Category Theory
Commutative Algebra
Homological Algebra
Real Analysis
Set Theory
- Cardinal Arithmetic, Cofinality and the Alephs
- Construction of the Natural Numbers
- Order, Zorn's Lemma, and the Axiom of Choice
- Ordinal Arithmetic and the First Uncountable Ordinal
- Ordinals, Cardinals, and Transfinite Recursion
- Relations, Functions, and Quotients
- The ZFC Axioms and the Basic Set Constructions
2 · Logical flowchart
3 · Items
Example
An internal shift reverses the published commutative twist parameter
Example
A right-flat tensor bimodule can have nonprojective output
Example
A left-projective tensor bimodule need not be right-flat
Sources
- Stacks Project, Algebra, §10.56, tag 00JL
- Alexander Kleshchev, Representation Theory of Symmetric Groups and Related Hecke Algebras (2009), §2.2, printed pp. 6-7
- Mikhail Khovanov and Paul Seidel, Quivers, Floer Cohomology, and Braid Group Actions, §§2a-2b, author pp. 8-9
- Charles A. Weibel, An Introduction to Homological Algebra, ch. 3, §3.2, printed pp. 68-69
- Stacks Project, Algebra, §10.12, tag 00CV