I am reading a book about linear algebra. On the basis of this book, I worked out the terminology below. Problem: To me, it looks like Wikipedia defines homomorphism differently. Apart from that: Do you agree with the following definitions of the homomorphism subtypes? If so, is there a trick to memorise them?
Let $V_1, V_2$ be vector spaces over a common field. We consider a function $f : V_1 \rightarrow V_2$. Now, $f$ is a homomorphism iff $f$ is linear (linear-algebra-linear, not calculus-linear).
epimorphism = homomorphism + surjective
monomorphism = homomorphism + injective
isomorphism = epimorphism + monomorphism
endomorphism = homomorphism + (domain = codomain)
automorphism = endomorphism + isomorphism
The article Algebra homomorphism enumerates (in its first sentence) homogeneity and additivity but also a third property. The third property seems to be missing in my definition (definition based on the book).
By the way, should I use the term map instead of function?