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13h
asked What are the universally effective epimorphisms of topological spaces?
15h
comment Functorial properties of the compact open topology.
In the category of Hausdorff spaces, a morphism is (isomorphic to) the inclusion of a closed subspace if and only if it is a regular monomorphism. Of course, right adjoints preserve regular monomorphisms. For general subspaces, you have to replace "regular monomorphism" with "extremal monomorphism".
15h
comment Functorial properties of the compact open topology.
There is an abstract nonsense argument for (2) in the case where $A$ is a closed subspace of $Y$. But I think it should also be true for non-closed subspaces.
15h
comment Functorial properties of the compact open topology.
(1) is indeed true by abstract nonsense, at least when the spaces concerned have the stated universal property.
23h
awarded  Enlightened
23h
awarded  Nice Answer
1d
revised Constructing a HoTT proof term of 1≠0
edited tags
1d
comment Disequality in Type Theory
Univalence is not needed for this proof.
1d
comment “Every function can be represented as a Fourier series”?
Yes, a function that has a Fourier series must be periodic. There are further conditions.
1d
comment How do I approach the classification problem?
There is no relation with the mathematical subject of category theory.
2d
comment Is the constant group scheme for $\mathbb{Z}$ affine?
Affine schemes are quasicompact. Is this quasicompact?
2d
comment Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
Categories and sheaves is quite difficult if you are not already familiar with categories, I think.
2d
comment Constructing a HoTT proof term of 1≠0
A similar point is described in the book, I think regarding the Boolean type. You should have a look.
Jul
28
answered Is taking projective closure a functor?
Jul
27
answered Does the inverse image sheaf have a left adjoint for $\mathsf{Set}$-valued sheaves?
Jul
27
revised Does the inverse image sheaf have a left adjoint for $\mathsf{Set}$-valued sheaves?
edited tags
Jul
27
comment Does an equivalence of $G$-sets and $H$-sets imply an isomorphism of $G$ and $H$?
Well, $G \cong G^\mathrm{op}$, so there's no real difference. But yes, in some sense it's really $G^\mathrm{op}$.
Jul
27
answered Does an equivalence of $G$-sets and $H$-sets imply an isomorphism of $G$ and $H$?
Jul
27
revised Does an equivalence of $G$-sets and $H$-sets imply an isomorphism of $G$ and $H$?
edited tags
Jul
27
comment Pullbacks in filtered categories?
Actually, you can replace condition 2 with "$\mathcal{D}$ is filtered".