What does $1 / \mathbf{Set}$ denote?
A pointed set is a set $X$ equipped with an element (a basepoint) $x \in X$. Let $\mathbf{Set_*}$ be the category of pointed sets and basepoint-preserving functions. Let $1$ be a one-element set. Show that $\mathbf{Set_*}$ is isomorphic to $1 / \mathbf{Set}$.
Question 3i on http://cheng.staff.shef.ac.uk/cat02/sheetone02.ps
It is the slice category (a special case of comma categories), sometimes also denoted by $\,1\!\downarrow {\bf Set}$, its objects are the arrows $1\to A$ of ${\bf Set}$ and its morphisms between $a:1\to A$ and $b:1\to B$ are arrows $f:A\to B$ that makes the triangle commutative, i.e. satisfying $\ f\circ a=b$.