24 Differential Graded Sheaves

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Section 24.1: Introduction
Section 24.2: Conventions
Section 24.3: Sheaves of graded algebras
- Definition 24.3.1
- Remark 24.3.2
Section 24.4: Sheaves of graded modules
- Definition 24.4.1
- Lemma 24.4.2
Section 24.5: The graded category of sheaves of graded modules
Section 24.6: Tensor product for sheaves of graded modules
Section 24.7: Internal hom for sheaves of graded modules
Section 24.8: Sheaves of graded bimodules and tensor-hom adjunction
- Definition 24.8.1
- Lemma 24.8.2
Section 24.9: Pull and push for sheaves of graded modules
- Lemma 24.9.1
Section 24.10: Localization and sheaves of graded modules
- Lemma 24.10.1
- Lemma 24.10.2
Section 24.11: Shift functors on sheaves of graded modules
- Lemma 24.11.1
Section 24.12: Sheaves of differential graded algebras
- Definition 24.12.1
- Remark 24.12.2
Section 24.13: Sheaves of differential graded modules
- Definition 24.13.1
- Lemma 24.13.2
  - Equation 24.13.2.1
Section 24.14: The differential graded category of modules
Section 24.15: Tensor product for sheaves of differential graded modules
Section 24.16: Internal hom for sheaves of differential graded modules
Section 24.17: Sheaves of differential graded bimodules and tensor-hom adjunction
- Definition 24.17.1
- Lemma 24.17.2
- Lemma 24.17.3
Section 24.18: Pull and push for sheaves of differential graded modules
- Lemma 24.18.1
Section 24.19: Localization and sheaves of differential graded modules
- Lemma 24.19.1
- Lemma 24.19.2
Section 24.20: Shift functors on sheaves of differential graded modules
Section 24.21: The homotopy category
- Definition 24.21.1
- Definition 24.21.2
- Lemma 24.21.3
Section 24.22: Cones and triangles
- Lemma 24.22.1
- Definition 24.22.2
- Lemma 24.22.3
- Proposition 24.22.4
- Remark 24.22.5
- Lemma 24.22.6
Section 24.23: Flat resolutions
- Lemma 24.23.1
- Lemma 24.23.2
- Lemma 24.23.3
- Lemma 24.23.4
- Remark 24.23.5
- Lemma 24.23.6
- Lemma 24.23.7
- Lemma 24.23.8
Section 24.24: The differential graded hull of a graded module
- Lemma 24.24.1
- Lemma 24.24.2
Section 24.25: K-injective differential graded modules
- Lemma 24.25.1
- Definition 24.25.2
- Remark 24.25.3
- Lemma 24.25.4
- Lemma 24.25.5
- Lemma 24.25.6
- Definition 24.25.7
- Lemma 24.25.8
- Lemma 24.25.9
- Lemma 24.25.10
- Lemma 24.25.11
- Lemma 24.25.12
- Theorem 24.25.13
Section 24.26: The derived category
- Lemma 24.26.1
- Lemma 24.26.2
- Lemma 24.26.3
- Definition 24.26.4
- Lemma 24.26.5
- Lemma 24.26.6
- Lemma 24.26.7
- Lemma 24.26.8
Section 24.27: The canonical delta-functor
- Lemma 24.27.1
- Lemma 24.27.2
Section 24.28: Derived pullback
- Equation 24.28.0.1
- Lemma 24.28.1
- Definition 24.28.2
- Lemma 24.28.3
- Lemma 24.28.4
- Lemma 24.28.5
- Lemma 24.28.6
- Lemma 24.28.7
Section 24.29: Derived pushforward
- Lemma 24.29.1
- Definition 24.29.2
- Lemma 24.29.3
- Lemma 24.29.4
  - Equation 24.29.4.1
- Lemma 24.29.5
- Lemma 24.29.6
- Lemma 24.29.7
- Lemma 24.29.8
- Lemma 24.29.9
Section 24.30: Equivalences of derived categories
- Lemma 24.30.1
Section 24.31: Resolutions of differential graded algebras
- Lemma 24.31.1
- Lemma 24.31.2
Section 24.32: Miscellany
Section 24.33: Differential graded modules on a category
- Definition 24.33.1
- Lemma 24.33.2
- Remark 24.33.3
- Lemma 24.33.4
Section 24.34: Differential graded modules on a category, bis
- Lemma 24.34.1
- Lemma 24.34.2
Section 24.35: Inverse systems of differential graded algebras
- Lemma 24.35.1
- Lemma 24.35.2
- Lemma 24.35.3 reference
- Proposition 24.35.4
- Remark 24.35.5