Category of Pointed Sets as Coslice Category

Theorem
Let $\mathbf{Set}_*$ be the category of pointed sets.

Let $\mathbf{Set}$ be the category of sets.

Let $1 := \left\{{*}\right\}$ be any singleton.

Then:


 * $\mathbf{Set}_* \cong 1 \mathop / \mathbf{Set}$

where $1 \mathop / \mathbf{Set}$ denotes the coslice of $\mathbf{Set}$ under $1$.