Definition : Let \(\mathcal{C}\) be a category and \(f:A\rightarrow C\) and \(g:B\rightarrow C\) be morphisms. We define pull back of \(f,g\) to be a triple \((P,f',g')\) where
  1. \(P\) is an object of \(\mathcal{C}\) and
  2. \(f':P\rightarrow B, g':P\rightarrow A\) with \(g\circ f'=f\circ g'\)
such that given any object \(P'\) of \(\mathcal{C}\) and morphisms \(g'':P'\rightarrow A\) and \(f'':P'\rightarrow B\) with \(g\circ f''=f\circ g''\), there exists a unique morphism \(\eta:P'\rightarrow P\) such that \(g''=g'\circ \eta\) and \(f''=f'\circ \eta\) as in the following commutative diagram. ql_9a65ff8c25615e2690891cb3f378db07_l3 Definition : Let \(\mathcal{C}\) be a category and \(f:A\rightarrow C\) and \(g:B\rightarrow C\) be morphisms. We define pull back of \(f,g\) to be a triple \((P,f',g')\) where
  1. \(P\) is an object of \(\mathcal{C}\) and
  2. \(f':P\rightarrow B, g':P\rightarrow A\) with \(g\circ f'=f\circ g'\)
such that given any object \(P'\) of \(\mathcal{C}\) and morphisms \(g'':P'\rightarrow A\) and \(f'':P'\rightarrow B\) with \(g\circ f''=f\circ g''\), there exists a unique morphism \(\eta:P'\rightarrow P\) such that \(g''=g'\circ \eta\) and \(f''=f'\circ \eta\) as in the following commutative diagram.