# Tagged Questions

**4**

votes

**4**answers

513 views

### What is the intuition of connections for cubical sets?

I am beggining to do some work with cubical sets and thought that I should have an understanding of various extra structures that one may put on cubical sets (for purposes of this question, ...

**25**

votes

**2**answers

2k views

### Intuition for coends

Let $D$ be a co-complete category and $C$ be a small category. For a functor $F:C^{op}\times C \to D$ one defines the co-end
$$
\int^{c\in C} F(c,c)
$$
as the co-equalizer of
$$
\coprod_{c\to ...

**4**

votes

**2**answers

545 views

### Intuition for the satellite of a functor

Occasionally in math I come across constructions or tools that are a bit convoluted. I can look at these constructions and see that they indeed perform the task they were made to do, but sometimes I ...

**28**

votes

**3**answers

2k views

### Why is there no Cayley's Theorem for rings?

Cayley's theorem makes groups nice: a closed set of bijections is a group and a group is a closed set of bijections- beautiful, natural and understandable canonically as symmetry. It is not so much a ...

**6**

votes

**4**answers

649 views

### What is the intuitive meaning of star and box in a pure type system?

The systems of the λ-cube have the axiom $\star:\square$.
I've listed a few meanings that the Curry-Howard isomorphism gives to $t : T$ below. What are the intuitive meanings of $\star$ and ...

**7**

votes

**2**answers

337 views

### Effects of “weak” vs. “strict” categories in Eckmann-Hilton arguments

A standard example for demonstrating the need for genuinely weak n-categories is that a weak 3-category with unique 0- and 1-cells amounts to the same thing as a braided monoidal category (by an ...

**5**

votes

**2**answers

369 views

### What are natural transformations in 1-categories?

It's well-known that, for lots of concrete categories (but by no means all), we can think of the objects as themselves being small categories, and morphisms are the functors between these categories. ...

**11**

votes

**5**answers

1k views

### Abstract nonsense versions of “combinatorial” group theory questions

In particular, I'm just curious whether there's a version of the Sylow theorems (which are very combinatorially-flavored) which allows horizontal and/or vertical categorification? Or at least can be ...

**52**

votes

**11**answers

9k views

### “Philosophical” meaning of the Yoneda Lemma

The Yoneda Lemma is a simple result of category theory, and its proof is very straightforward.
Yet I feel like I do not truly understand what it is about; I have seen a few comments here mentioning ...