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Results tagged with higher-category-theory
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user 98306
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
3
votes
Can $\mathsf{Set}$ be seen as a (non-trivial) 2-category?
There is a (not very interesting) construction which works for every category $\mathcal{C}$: Take any commutative monoid $M$. For parallel morphisms $f,g$ we define a $2$-morphism $f \to g$ to be some …
- 5,482
0
votes
Accepted
Equality of lax natural transformations in the constructive approach
A more simple question would be (and this is the special case $\mathbf{C}=1$): When are two functors $F,G : \mathcal{C} \to \mathcal{D}$ between $1$-categories $\mathcal{C},\mathcal{D}$ equal? Since w …
- 5,482
11
votes
Is it always possible to write a scheme as a colimit of affine schemes?
Actually, every scheme is the canonical colimit of all affine schemes mapping into it:
$$X = \underset{\substack{U \to X\\U \text{ affine}}}{\mathrm{colim}} U$$
In order to avoid size issues, we can i …
- 5,482
4
votes
What's the (monoidal) image of a monoidal functor?
Let $F : \mathcal{C} \to \mathcal{D}$ be a strong monoidal functor. Since monoidal categories are non-strict structures in the sense that e.g. associativity of $\otimes$ only holds up to isomorphism, …
- 5,482