Category:Set Products

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This category contains results about Set Products.

Let $S$ and $T$ be sets.

Let $P$ be a set and let $\phi_1: P \to S$ and $\phi_2: P \to T$ be mappings such that:

For all sets $X$ and all mappings $f_1: X \to S$ and $f_2: X \to T$ there exists a unique mapping $h: X \to P$ such that:
$\phi_1 \circ h = f_1$
$\phi_2 \circ h = f_2$
that is, such that:
$\begin{xy}\[email protected][email protected]+3px{ & X \ar[ld]_*+{f_1} \[email protected]{-->}[d]^*+{h} \ar[rd]^*+{f_2} \\ S & P \ar[l]^*+{\phi_1} \ar[r]_*+{\phi_2} & T }\end{xy}$
is a commutative diagram.

Then $P$, together with the mappings $\phi_1$ and $\phi_2$, is called a product of $S$ and $T$.


This category has only the following subcategory.