I was reading these notes on Category Theory and it said (paraphrased to add context):
Exercise 4: Explain why in Set (the Category of Sets), the product of an empty set of sets is a one-element set.
which I think is incorrect. The product of two empty sets (or any number) is empty because we are considering:
$$ \emptyset \times \emptyset = \{ (a,b) : a \in \emptyset, b \in \emptyset \} = \emptyset$$
where $a \in \emptyset , b \in \emptyset$ are false, so the above is the $\emptyset$ which is NOT a one element set (its a zero element set).
This should be trivial so I am assuming I am somewhere mis reading the natural language of the exercise. Someone help me catch where is it? i.e whats being asked and what the answer is?