Topological Sum is Coproduct in Category of Topological Spaces
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Theorem
Let $\mathbf{Top}$ be the category of topological spaces.
Let $X$ and $Y$ be topological spaces, and let $X \sqcup Y$ be their topological sum.
Then $X \sqcup Y$ is the coproduct of $X$ and $Y$ in $\mathbf{Top}$.
Proof
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Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 3.2$: Example $3.6$