If S⪧JXS \mathbin{⪧}_J XS⪧JX and f:Y→Xf : Y \to Xf:Y→X, then f∗(S)⪧JYf^*(S) \mathbin{⪧}_J Yf∗(S)⪧JY f∗(S)f^*(S)f∗(S) defined by f∗(S):={g:Z→Y∣f∘g∈S}f^*(S) := \{ g : Z \to Y \mid f \circ g \in S \}f∗(S):={g:Z→Y∣f∘g∈S} We can represent it as
