DefinitionEquivalent arrows

Two arrows \(\Arrow{A}{B}\) and \(\Arrow{X}{Y}\), joining

\(A(a_1,\dots ,a_n)\)

to

\(B(b_1,\dots ,b_n)\)

\(X(x_1,\dots ,x_n)\)

to

\(Y(y_1,\dots ,y_n)\)

are called equivalent if

\((b_1-a_1,\dots ,b_n-a_n)\)\(=\)\((y_1-x_1,\dots ,y_n-x_n)\)