Definition:Coproduct/Sets
< Definition:Coproduct(Redirected from Definition:Set Coproduct)
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Definition
Let $S_1$ and $S_2$ be sets.
A coproduct $\struct {C, i_1, i_2}$ of $S_1$ and $S_2$ comprises a set $C$ together with mappings $i_1: S_1 \to C$, $i_2: S_2 \to C$ such that:
Hence:
- $\begin{xy} \xymatrix@L+2mu@+1em{ & C \ar@{-->}[dd]_*{h} & \\ S_1 \ar[ru]^*{i_1} \ar[rd]_*{f_1} & & S_2 \ar[lu]_*{i_2} \ar[ld]^*{f_2} \\ & X & }\end{xy}$
- is a commutative diagram.
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 5$. Induced mappings; composition; injections; surjections; bijections: Exercise $18$