Engineering↗
Completions of Filtrations and lim1
Inverse limits and their failure of exactness, the derived functor lim^1, the Mittag-Leffler condition, the Milnor sequence, and completion of filtered objects.
Tag
Spectral Sequences
Every page in the KEVOS library tagged Spectral Sequences. 7 pages.
Engineering↗
Convergence of Spectral Sequences
Convergence conditions for spectral sequences, first-quadrant and bounded cases, conditional convergence, and the failure modes including non-vanishing lim^1.
Engineering↗
Exact Couples and Spectral Sequences
Spectral sequences as successive approximations, pages and differentials, exact couples and their derivation, and the standard sources of spectral sequences.
Engineering↗
Filtered Differential Objects
Filtrations of chain complexes, the associated graded object, the spectral sequence of a filtered complex, and the interpretation of the pages.
Engineering↗
The Grothendieck Spectral Sequence
The Grothendieck spectral sequence for a composite of functors, the acyclicity hypothesis, the five-term sequence and edge maps, and the standard specialisations.
Engineering↗
The Ladder of an Exact Couple and Rees Systems
The ladder diagram of an exact couple, Rees systems, and the systematic treatment of filtered chain complexes and their limits.
Engineering↗
The Lyndon–Hochschild–Serre Spectral Sequence
The LHS spectral sequence for a normal subgroup, its E2 page, the action of the quotient, the five-term sequence, and worked applications.
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