Alphabeta MathDouble Complexes Exact Couples and Convergence — Examples
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1 · Prerequisites
Abstract Algebra
Category Theory
Homological Algebra
Number Theory
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
The two spectral sequences of a two by two double complex
Example
Acyclic assembly with exact columns
Example
The exact couple of a two step filtration
Example
Deriving an exact couple once
Example
A first quadrant five term exact sequence
Counterexample
Sum and product totalisations on an infinite diagonal
Counterexample
An exhaustive nonseparated filtration with the wrong naive abutment
Example