nLab
substitution natural deduction - table

type theorycategory theory
syntaxsemantics
natural deductionuniversal construction
substitution…………………….pullback
x 2:X 2A(x 2):Typex 1:X 1f(x 1):X 2x 1:X 1A(f(x 1)):Type\frac{ x_2 \colon X_2\; \vdash\; A(x_2) \colon Type \;\;\;\; x_1 \colon X_1\; \vdash \; f(x_1)\colon X_2}{ x_1 \colon X_1 \;\vdash A(f(x_1)) \colon Type}\, f *A A X 1 f X 2\array{ f^* A &\to& A \\ \downarrow && \downarrow \\ X_1 &\stackrel{f}{\to}& X_2 }
Revised on November 14, 2012 22:38:09 by Stephan Alexander Spahn (79.227.144.65)