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I am a 9th grader self-studying about set theory and functions. I understood most basic concepts, but I didn't understand what is a surjective function. I have understood what is an injective funct...

Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is …

Understanding the definition of surjective function Ask Question Asked 7 years, 11 months ago Modified 7 years, 11 months ago

Here you don't care about domains and codomains. This is often good enough for practical considerations. But from the formal viewpoint, it doesn't make sense to ask whether this …

Jun 16, 2017 · Whether or not a function like that is surjective becomes an interesting question, not only for solving equations, but for answering other questions about the structure of the …

I have the same feeling as yours: often, proving that a linear map is injective is easier than proving it is surjective. Of course we are talking about infinite-dimensional vector spaces, otherwise …

Sep 25, 2016 · The proof in the book said out of nowhere that $g (f (x))$ is surjective, something introduced only a few seconds ago so I had to go back to the definition of surjective.

Oct 24, 2020 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …

I want to prove that surjectivity is stable under base change: if $f:X\to S$ a surjective morphism of scheme and $\varphi:T\to S$ then $f_T:X\times_S T\to T$ is surjective.