Aditive functor characterization. Aditive iff right/left exact.
123242
Half exact functor which is neither right exact nor left exact
38691
Injectivity of Homomorphism in Localization
25260
Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
74617
Equivalent conditions for a preabelian category to be abelian
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
7441
Hom is a left-exact functor
129858
"Almost" ring homomorphism
48990
Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
85148
How do ideal quotients behave with respect to localization?
42941
Pair of adjoint functors and showing that two certain maps are inverses
69160
Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
44258
Conditions under which group solvability is invariant under an homomorphism.
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
63146
Proof of properties of injective and surjective functions.
29756
Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice