導出函子
- Understand how derived functors relate the three-cycle and the foursome.
- Understand how derived functors relate the four functors on sheaves to the foursome
- Understand how setting {$R^2F=0$} yields the gradation and the eightfold way.
- What does it mean to compute the cohomology at the {$i$}th spot? This yields {$RF$}.
读物
- 维基百科: Derived functor
- A circulation - a three-cycle - is a self-adjoint functor which constructs itself as it goes along.
Threesome, zigzag lemma, derived functors
Derived functors.
- The above-mentioned property of turning short exact sequences into long exact sequences is a consequence of the snake lemma.
Threesome
- Does the super Jacobi identity have any significance?
- Let {$ p:E\to B$} be a basepoint-preserving Serre fibration with fiber {$F$}, that is, a map possessing the homotopy lifting property with respect to CW complexes. Suppose that B is path-connected. Then there is a long exact sequence of homotopy groups ... Infinite three-cycle.
- Cross product as example of Jacobi identity and three-cycle.
- Learning strips off deviation one dimension at a time, as in homology, long exact sequences.