6 Sheaves on Spaces

Section 6.1: Introduction
Section 6.2: Basic notions
Section 6.3: Presheaves
- Definition 6.3.1
- Definition 6.3.2
Section 6.4: Abelian presheaves
- Example 6.4.1
- Lemma 6.4.2
- Lemma 6.4.3
- Definition 6.4.4
- Example 6.4.5
Section 6.5: Presheaves of algebraic structures
- Definition 6.5.1
- Definition 6.5.2
Section 6.6: Presheaves of modules
- Definition 6.6.1
- Lemma 6.6.2
Section 6.7: Sheaves
- Definition 6.7.1
- Remark 6.7.2
- Example 6.7.3
- Definition 6.7.4
- Example 6.7.5
- Example 6.7.6
Section 6.8: Abelian sheaves
- Definition 6.8.1
Section 6.9: Sheaves of algebraic structures
- Definition 6.9.1
- Lemma 6.9.2
- Example 6.9.3
- Example 6.9.4
Section 6.10: Sheaves of modules
- Definition 6.10.1
Section 6.11: Stalks
- Lemma 6.11.1
- Definition 6.11.2
- Example 6.11.3
- Example 6.11.4
- Example 6.11.5
Section 6.12: Stalks of abelian presheaves
- Lemma 6.12.1
Section 6.13: Stalks of presheaves of algebraic structures
- Lemma 6.13.1
Section 6.14: Stalks of presheaves of modules
- Lemma 6.14.1
- Lemma 6.14.2
Section 6.15: Algebraic structures
- Definition 6.15.1
- Lemma 6.15.2
- Lemma 6.15.3
- Lemma 6.15.4
- Example 6.15.5
- Example 6.15.6
Section 6.16: Exactness and points
- Lemma 6.16.1
- Definition 6.16.2
- Lemma 6.16.3
- Lemma 6.16.4
Section 6.17: Sheafification
- Lemma 6.17.1
- Lemma 6.17.2
- Lemma 6.17.3
- Example 6.17.4
- Lemma 6.17.5
Section 6.18: Sheafification of abelian presheaves
- Lemma 6.18.1
- Lemma 6.18.2
Section 6.19: Sheafification of presheaves of algebraic structures
- Lemma 6.19.1
Section 6.20: Sheafification of presheaves of modules
- Lemma 6.20.1
- Lemma 6.20.2
- Lemma 6.20.3
Section 6.21: Continuous maps and sheaves
- Lemma 6.21.1
- Lemma 6.21.2
- Lemma 6.21.3
- Lemma 6.21.4
- Lemma 6.21.5
- Lemma 6.21.6
- Definition 6.21.7
- Lemma 6.21.8
- Definition 6.21.9
- Lemma 6.21.10
Section 6.22: Continuous maps and abelian sheaves
- Lemma 6.22.1
Section 6.23: Continuous maps and sheaves of algebraic structures
- Lemma 6.23.1
Section 6.24: Continuous maps and sheaves of modules
- Lemma 6.24.1
- Lemma 6.24.2
- Lemma 6.24.3
- Lemma 6.24.4
- Lemma 6.24.5
- Lemma 6.24.6
- Lemma 6.24.7
- Lemma 6.24.8
Section 6.25: Ringed spaces
- Definition 6.25.1
- Example 6.25.2
- Definition 6.25.3
Section 6.26: Morphisms of ringed spaces and modules
- Definition 6.26.1
- Lemma 6.26.2
- Lemma 6.26.3
- Lemma 6.26.4
Section 6.27: Skyscraper sheaves and stalks
- Definition 6.27.1
- Lemma 6.27.2
- Lemma 6.27.3
Section 6.28: Limits and colimits of presheaves
Section 6.29: Limits and colimits of sheaves
- Lemma 6.29.1
- Example 6.29.2
- Lemma 6.29.3
- Lemma 6.29.4
Section 6.30: Bases and sheaves
- Definition 6.30.1
- Definition 6.30.2
- Lemma 6.30.3
- Lemma 6.30.4
- Lemma 6.30.5
- Lemma 6.30.6
- Lemma 6.30.7
- Definition 6.30.8
- Lemma 6.30.9
- Lemma 6.30.10
- Definition 6.30.11
- Lemma 6.30.12
- Lemma 6.30.13
- Lemma 6.30.14
- Lemma 6.30.15
- Lemma 6.30.16
- Lemma 6.30.17
Section 6.31: Open immersions and (pre)sheaves
- Lemma 6.31.1
- Definition 6.31.2
- Definition 6.31.3
- Lemma 6.31.4
- Definition 6.31.5
- Lemma 6.31.6
- Lemma 6.31.7
- Lemma 6.31.8
- Lemma 6.31.9
- Lemma 6.31.10
- Lemma 6.31.11
- Lemma 6.31.12
- Remark 6.31.13
Section 6.32: Closed immersions and (pre)sheaves
- Lemma 6.32.1
- Lemma 6.32.2
- Lemma 6.32.3
- Lemma 6.32.4
- Remark 6.32.5
- Remark 6.32.6
Section 6.33: Glueing sheaves
- Lemma 6.33.1
- Lemma 6.33.2
- Lemma 6.33.3
- Lemma 6.33.4