Idea Broad idea The Green-Schwarz action functional is an action functional for a sigma-model that describes the propagation of a fundamental super pp-brane Σ\Sigma in a super spacetime supermanifold. For p=0p = 0 this is the Green-Schwarz superparticle. For p=1p = 1 this is the Green-Schwarz superstring (Green-Schwarz 84) For p=2p =2 this is the Green-Schwarz supermembrane (Bergshoeff-Sezgin-Town
Moreover, for f:X→Yf : X \to Y a morphism in CC, this induces a natural transformation h f:h X→h Yh_f : h_X \to h_Y, whose component on UU in XX is illustrated by For this to be a natural transformation, we need to have the commuting diagram h XU →h fU h YU h Xα↓ ↓h Yα h XU′ →h fU′ h YU′\array{ h_X U & \stackrel{h_f U}{\rightarrow} & h_Y U \\ \mathllap{h_X\alpha\quad}{\downarrow} & {} & \mathrlap{
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