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Aug
1
comment Uncountable Kronecker Delta?
You can certainly define $\delta$ for arbitrary index sets. Continuity has nothing to do with it.
Aug
1
comment How to compute (co)limits of enriched categories?
(1) is not the cartesian product. It is the tensor product. The cartesian product has hom-objects given by cartesian products, of course.
Aug
1
comment Are there any free or fascist boolean algebras?
The category of boolean algebras is a full reflective subcategory of the category of Heyting algebras, by a very standard argument.
Jul
31
comment How to compute (co)limits of enriched categories?
As for whether $\mathcal{V}\textbf{-Cat}$ is cocomplete – that's true, but it's hard. See [Wolff, $\mathcal{V}\textbf{-Cat}$ and $\mathcal{V}\textbf{-Graph}$].
Jul
31
comment How to compute (co)limits of enriched categories?
Coproducts are easy, of course. But as you say, coequalisers are hard, and if you can't figure that out (even for $\mathcal{V} = \mathbf{Set}$), you don't have a general formula.
Jul
31
comment How to compute (co)limits of enriched categories?
There is no general formula. Even colimits of ordinary categories are hard. Incidentally, (a) is not always the cartesian product.
Jul
30
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".
Jul
30
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.
Jul
30
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.
Jul
30
comment Disequality in Type Theory
Univalence is not needed for this proof.
Jul
30
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.
Jul
29
comment How do I approach the classification problem?
There is no relation with the mathematical subject of category theory.
Jul
29
comment Is the constant group scheme for $\mathbb{Z}$ affine?
Affine schemes are quasicompact. Is this quasicompact?
Jul
28
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.
Jul
28
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
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
comment Pullbacks in filtered categories?
Actually, you can replace condition 2 with "$\mathcal{D}$ is filtered".
Jul
27
comment topos have colimits
There is no reason to expect an elementary proof. Category theory may be abstract nonsense but it does simplify things sometimes.
Jul
26
comment topos have colimits
You should learn about monads. The concrete details are painful even in the case of the initial object: see here.
Jul
26
comment coherence of inverses in 2-groupoids
1-cell inversion acts on 2-cells. In fact, the natural operation sends a 2-cell $f \Rightarrow g$ to a 2-cell $g^{-1} \Rightarrow f^{-1}$.