X⊗(Y⊗Z)tensor-product𝑋tensor-product𝑌𝑍{{X\otimes(Y\otimes Z)}}X⊗(Z⊗Y)tensor-product𝑋tensor-product𝑍𝑌{{X\otimes(Z\otimes Y)}}(X⊗Y)⊗Ztensor-producttensor-product𝑋𝑌𝑍{{(X\otimes Y)\otimes Z}}(X⊗Z)⊗Ytensor-producttensor-product𝑋𝑍𝑌{{(X\otimes Z)\otimes Y}}Z⊗(X⊗Y)tensor-product𝑍tensor-product𝑋𝑌{{Z\otimes(X\otimes Y)}}(Z⊗X)⊗Ytensor-producttensor-product𝑍𝑋𝑌{{(Z\otimes X)\otimes Y}}mathrmidifx..⋄lsei⊗βY,Z\scriptstyle{mathrm{id}{ifx..lse\par i}\otimes\beta_{Y,Z}}αX,Y,Zsubscript𝛼𝑋𝑌𝑍\scriptstyle{\alpha_{X,Y,Z}}αX,Z,Ysubscript𝛼𝑋𝑍𝑌\scriptstyle{\alpha_{X,Z,Y}}βX⊗Y,Zsubscript𝛽tensor-product𝑋𝑌𝑍\scriptstyle{\beta_{X\otimes Y,Z}}βX,Z⊗mathrmidifx..⋄lsei\scriptstyle{\beta_{X,Z}\otimes mathrm{id}{ifx..lse\par i}}αZ,X,Ysubscript𝛼𝑍𝑋𝑌\scriptstyle{\alpha_{Z,X,Y}}
(X⊗Y)⊗Ztensor-producttensor-product𝑋𝑌𝑍{{(X\otimes Y)\otimes Z}}(Y⊗X)⊗Ztensor-producttensor-product𝑌𝑋𝑍{{(Y\otimes X)\otimes Z}}X⊗(Y⊗Z)tensor-product𝑋tensor-product𝑌𝑍{{X\otimes(Y\otimes Z)}}Y⊗(X⊗Z)tensor-product𝑌tensor-product𝑋𝑍{{Y\otimes(X\otimes Z)}}(Y⊗Z)⊗Xtensor-producttensor-product𝑌𝑍𝑋{{(Y\otimes Z)\otimes X}}Y⊗(Z⊗X)tensor-product𝑌tensor-product𝑍𝑋{{Y\otimes(Z\otimes X)}}βX,Y⊗mathrmidifx..⋄lsei\scriptstyle{\beta_{X,Y}\otimes mathrm{id}{ifx..lse\par i}}αX,Y,Z−1subscriptsuperscript𝛼1𝑋𝑌𝑍\scriptstyle{\alpha^{-1}_{X,Y,Z}}αY,X,Z−1subscriptsuperscript𝛼1𝑌𝑋𝑍\scriptstyle{\alpha^{-1}_{Y,X,Z}}βX,Y⊗Zsubscript𝛽𝑋tensor-product𝑌𝑍\scriptstyle{\beta_{X,Y\otimes Z}}mathrmidifx..⋄lsei⊗βX,Y\scriptstyle{mathrm{id}{ifx..lse\par i}\otimes\beta_{X,Y}}αY,Z,X−1subscriptsuperscript𝛼1𝑌𝑍𝑋\scriptstyle{\alpha^{-1}_{Y,Z,X}}