Can a functor $ F: A\to B$ not map $A$ to a subcategory of $B$?
80260
Can it happen that the image of a functor is not a category?
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
121945
Monomorphisms and Epimorphisms in the category of small categories
55778
Group theoretic meaning of natural isomorphisms between certain functors
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
57519
What is the opposite category of $\operatorname{Top}$?
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
94165
Why is a map to a smaller dimensional space not injective?
27400
About Baire's Category Theorem(BCT)
150961
An example for a homomorphism that is not an automorphism
40793
What is the difference betwen equivalence and isomorphism of functors in categories.
151575
Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
140503
What properties do natural isomorphisms between functors preserve?
118154
$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice
99671
Are surjective sheaf morphisms locally surjective?
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin