Pullback Map

A pullback is a general Categorical operation appearing in a number of mathematical contexts, sometimesgoing under a different name. If is a linear transformation between Vector Spaces,then (usually called Transpose Map or Dual Map because its associated matrix is theMatrix Transpose of ) is an example of a pullback map.

In the case of a Diffeomorphism and Differentiable Manifold, a very explicit definition can be formulated.Given an -form on a Manifold , define the -form on by its action on an -tupleof tangent vectors as the number . Thisdefines a map on -forms and is the pullback map.

• Ruler Function
• Ruling
• Run
• Runge-Kutta Method
• Runge-Walsh Theorem
• Running Knot
• Russell's Antinomy
• Russell's Paradox
• Russian Multiplication
• Russian Roulette
• Ryser Formula
• Rényi's Parking Constants
• Rössler Model
• Saalschützian
• Saalschütz's Theorem
• s-Additive Sequence
• Saddle
• Saddle-Node Bifurcation
• Saddle Point (Fixed Point)
• Saddle Point (Function)
• Saddle Point (Game)
• Safarevich Conjecture
• Safe
• Sagitta
• Saint Andrew's Cross