Product Map (積写像) (Definition IV.5.3)
- Product Map (積写像) (Definition IV.5.3) #Card
- Given $f_j : V_j \to X_j$, the product map $\prod_{j \in J} f_j : \prod_j V_j \to \prod_j X_j$ is defined factor-wise: $(p_j \circ \prod_k f_k)(\varphi) := f_j(\varphi(j))$.
Given $f_j : V_j \to X_j$ for each $j \in J$, the product map $$\prod_{j \in J} f_j : \prod_{j \in J} V_j \to \prod_{j \in J} X_j$$ is defined factor-wise by $(p_j \circ \prod_{k \in J} f_k)(\varphi) := f_j(\varphi(j))$.
- 2 変数の場合: $(f_0 \times f_1)(v_0, v_1) = (f_0(v_0), f_1(v_1))$。
- 対角積写像 cards/topology/diagonal-product-map（共通の定義域）と混同しないこと: $\triangle_{j} f_j = (\prod_j f_j) \circ \triangle$。
Prod.map f₀ f₁；依存版は fun φ j => f j (φ j)