Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

As I understand it, in the category of sets, there is no morphism $\{1\}\rightarrow\emptyset$. On the other hand, is one permitted to say sentences like the following?

"Consider the empty family $(\phi_\alpha)_\alpha$ of morphisms, where $\phi_\alpha:\{1\}\rightarrow\emptyset$."

For example, can one say,

"Find the pullback of the empty family $(\phi_\alpha)_\alpha$ of morphisms, where $\phi_\alpha:\{1\}\rightarrow\emptyset$."

share|improve this question
add comment

1 Answer 1

up vote 4 down vote accepted

Sure. There's still a perfectly well-defined universal property (it's just vacuous) and a perfectly well-defined universal object satisfying it (exercise).

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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