Exact Sequence

★★★★☆Undergraduate

📖Definition

Sequence of maps where image at each position equals kernel of next map

📐Formulas

...→ A →^f B →^g C →...
im f = ker g
Short exact: 0 → A → B → C → 0

✏️Examples

예제 1

0 → ℤ →^{×2} ℤ → ℤ/2ℤ → 0

예제 2

Split exact sequence

Applications

Extension problems

Homology

Algebraic K-theory

🔗Related Documents

Applications

#완전열#exact#sequence#kernel