lemma A.71 The pullback is an algebra map commuting with $\dd$

Rests on

• depends_on definition A.70 Pullback ¶
  • depends_on definition 7.97 Partial derivative; gradient ¶
    • depends_on definition 7.26 Derivative of a function at a point ¶
      • depends_on definition 7.16 Limit ¶
        • depends_on definition 7.2 Absolute value ¶
        • depends_on definition 7.9 Real function ¶
      • depends_on definition 7.9 Real function ¶ ↺
    • depends_on definition 5.15 Basis ¶
      • depends_on definition 5.12 Subspace generated by a set of vectors ¶
        • depends_on definition 5.5 Linear combination ¶
        • depends_on definition 5.7 Vector subspace ¶
        • proves proof ch:03-linear-algebra-representations@proof-3 ¶
      • depends_on definition 5.14 Linear independence ¶
        • depends_on definition 5.5 Linear combination ¶ ↺
  • depends_on definition 13.83 Covector ¶
    • depends_on definition 13.81 Vector on a manifold ¶
      • depends_on definition 13.71 Differentiable curve ¶
        • depends_on definition 13.48 Differentiable manifold ¶
      • depends_on definition 13.45 Differentiable map on a topological space ¶
        • depends_on definition 13.44 Atlas ¶
        • depends_on definition 13.43 Coordinate system ¶
      • depends_on definition 13.48 Differentiable manifold ¶ ↺
  • depends_on definition 13.98 $k$-form ¶
    • depends_on definition 13.83 Covector ¶ ↺
    • depends_on definition 13.84 Tensor ¶
      • depends_on definition 13.83 Covector ¶ ↺
      • depends_on definition 13.81 Vector on a manifold ¶ ↺
• depends_on equation 13.246 eq:mfd-leibniz-forms ¶
• depends_on equation 13.245 eq:mfd-nilpotency ¶
• proves proof app:A-long-proofs@proof-51 ¶

Supports

Nothing declares a dependency on this node yet.