Reputation
18,543
Top tag
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
1 17 45
Newest
 Enlightened
Impact
~204k people reached

1d
awarded  Enlightened
1d
awarded  Nice Answer
2d
comment Metrics and Measures on a Category of Cats : a cauchy complete category of categories
These questions are getting a bit repetitive. Do you have some overarching goal you'd like to share?
Feb
10
answered On the definition of double categories?
Feb
9
comment The magic of the morphisms
It's just what a concrete category is. It's a fine point, but it seems unlikely that, for instance, you could prove theorems about spotted sets.
Feb
9
comment The magic of the morphisms
But I'm saying that the structures really aren't different. Yes, a topology is a special kind of spotted set. So what? It seems like you're basically making the observation that many objects are defined as structured sets, and that the structure on a set usually comes from a subset of a related set.
Feb
9
comment The magic of the morphisms
I'm not sure in what sense this is a coincidence. It's not a very drastic reframing of the explicit definition of continuous functions.
Feb
8
comment Is it accurate to say that multiplication of two integers yields an integer?
I don't think this looks relevant to the question.
Feb
7
comment Correct definition of model category
He discusses the choice of the functorial factorization in the book, as I recall, and uses it constantly, for instance in getting to his main results about every homotopy category being a module over the classical homotopy category.
Feb
6
comment Is there a reasonable Grothendieck topology on the category of modules over a ring?
There are more describable choices than just these extrema. Perhaps the most natural topology is the regular topology, which in this case just has coverings generated by epimorphisms. Still not exciting, of course.
Feb
4
revised Is there any comprehensive definition of the opposite category $\mathcal C^{op}$ of a category $\mathcal C$?
added 2 characters in body
Feb
4
comment Is there any comprehensive definition of the opposite category $\mathcal C^{op}$ of a category $\mathcal C$?
Hah, good point, don't know why I did that.
Feb
4
answered Is there any comprehensive definition of the opposite category $\mathcal C^{op}$ of a category $\mathcal C$?
Feb
2
comment Is this definition of $(c\downarrow G)$ the slice category or is it something else?
Any explanation for the downvote?
Feb
1
answered Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?
Jan
31
answered Is this definition of $(c\downarrow G)$ the slice category or is it something else?
Jan
29
comment How are non-bijective morphisms “reversed”?
@goblin have you tried looking up the word? It's very simple, just an inverse limit of finite discrete topological rings.
Jan
28
comment Automorphism of a category sends objects to isomorphic objects?
Just to note that you can get the kind of thing you're looking for from automorphisms (and autoequivalences) naturally isomorphic to the identity.
Jan
28
comment In what sense right dual and braiding structure respect the tensor product structure in a monoidal category?
I don't quite understand whether you have another question.
Jan
28
comment In what sense right dual and braiding structure respect the tensor product structure in a monoidal category?
It's a natural transformation such that (all the braid relations.)