I need to prove that exists a homomorphism uniquely determined in a exact sequence
53548
$M' \to M \to M'' \to 0$ exact $\implies 0\to \text{Hom}(M'',N) \to \text{Hom}(M,N) \to \text{Hom}(M',N)$ is exact.
141895
Proving that a sequence is monotone
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
158882
Prove the existence of some weird family of sets
136167
Prove that structure $(Q/{0}; =;*)$ has infinite number of automorphisms
111743
In a ring homomorphism we always have $f(1)=1$?
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
33455
Question on group homomorphisms involving the standard Z-basis
44396
Noetherian Ring under a Homomorphism / homomorphic function / map
120002
Prove universal morphism is unique up to unique isomorphism.
150385
The use of the Axiom of Choice in this proof of the sequence lemma
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
139828
Finitely Presented Modules and Exact Sequences
114522
Prove that identity is unique in a group
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.