Why is the categorical quotient unique?
120002
Prove universal morphism is unique up to unique isomorphism.
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
56528
On the proof of existence and uniqueness of radix representation
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
85148
How do ideal quotients behave with respect to localization?
54333
In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?
138569
Is the “sum of all natural numbers” unique?
34300
"Natural" categories where monomorphisms differ from injective morphisms
121945
Monomorphisms and Epimorphisms in the category of small categories
53418
Why finite structures are uniquely characterized?
142652
When is the product of two quotient maps a quotient map?
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
46408
Show that the Hausdorff topology is unique in a finite set $X$
27400
About Baire's Category Theorem(BCT)
117187
Uniqueness of the involution on a $C^*$-algebra
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$