Why the presheaf image of an injective morphism of sheaves is automatically a sheaf?
40427
Presheaf image of a monomorphism of sheaves is a sheaf
87412
when does a functor map products into products?
115088
Surjective morphism of affine varieties and dimension
67948
Why are continuous functions the "right" morphisms between topological spaces?
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
157054
Long exact sequence in homology: naturality=functoriality?
97810
bijective morphism of affine schemes
46875
The identity morphism in $\mathbf{Set}$ is the identity function
143043
When is a local homeomorphism a covering map?
8654
Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.
34909
To what extent is a scheme morphism determined by its topological map?
69367
covering map with finite fibres and preimage of a compact set
152354
Why is an empty set not a terminal object in categories $\mathsf{Top}$ and $\mathsf{Sets}$?
9793
Why is the image of a smooth embedding $f: N \to M$ an embedded submanifold?
68786
"This property is local on" : properties of morphisms of $S$-schemes
40678
Image of an ideal under a surjective ring homomorphism is an ideal
116350
First axiom of sheaves: in noetherian topological spaces the direct limit presheaf is a sheaf.