I am currently reading Spivak's "Category Theory for the Sciences", and on page 16 the following definition is given:

Let $X$ and $Y$ be sets. We write $Hom_{Set}(X, Y)$ to denote the set of functions $X \rightarrow Y$.

Exercise is to "Find a set $B$ such that for all sets $X$ there is exactly one element in $Hom_{Set}(B, X)$."

And the provided answer is $B=\emptyset$.

Is the single function the "empty function"?


Yes, it is indeed the empty function.${}{}{}{}$. In this case, the empty set is said to be initial.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.