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Feb
11
comment Metrics and Measures on a Category of Cats : a cauchy complete category of categories
I guess I will take this to math overflow.
Feb
11
comment Metrics and Measures on a Category of Cats : a cauchy complete category of categories
I will add what i can to to my question here.
Feb
10
comment A complete category of categories and embeddings
Hi @Oskar, I am trying to do a calculation which is the calculation of colimits in Cat (and have been advised to do it with coproducts and coequalizers). Here is a link to my explanation page at nforum. I really need help doing the calculation, so if you would like to help, that would be great!
Feb
9
comment A complete category of categories and embeddings
Amazing and very helpful thanks so much!
Feb
8
comment What functors are these?
Yes, ok, the idea isn't totally general. But can we define $A$ such that the functor exists? In that case, how do we see such a functor?
Feb
8
comment What functors are these?
Suppose you have a monoid, with a partial composition (not all elements compose) and you then define equations over words in your "partial monoid". If you had a finite presentation of your partial monoid, you should have some set of equations that define it. The same is true for "just arrow" categories.
Feb
8
comment What functors are these?
Perhaps I need to start there, and ask "given a just arrow category, C, can we have the set of equations for C?"
Feb
8
comment What functors are these?
I will try to be more explicit, but please read the link in the post.
Sep
14
comment Categories of categories where large objects are colimits over small objects
Hi, I am now wondering about a host category for your suggestion. That is, what kind of category has, as objects, large categories like Hilb and Group, as well as all their finitely generated subcategories? Also, do you have a reference for your stated theorem?
Sep
13
comment Categories of categories where large objects are colimits over small objects
Hi, according to this definition, a locally presentable category would have only small objects. I am deducing from this that any locally presentable category of categories can only have small categories as objects.
Mar
2
comment Examples of colimits in a category of categories
Hi Ben, you have mentioned a motivating example. Before I was thinking about colimits in a category of categories, I was thinking about groups presented with generators and relations. In the category you talk about, we see that the finitely presentable categories form diagrams. These diagrams have colimits which are other groups that are not finitely presentable. The arrow between groups goes from one group to another group with the same axioms plus one or more extra axioms. Thus, the finitely presentable groups are approximations to groups that have no finite presentation.
Feb
27
comment Are these endofunctor categories compactly accessible? (Given a suitable base…)
Thanks again for your help here. I am going to revisit my definition for the functor, probably taking into account the tensor product...back to the drawing board
Feb
25
comment Are these endofunctor categories compactly accessible? (Given a suitable base…)
In that subcategory of CHU I linked to, we have a monoidal product. So, I am interested in functors with the following property. Given a compound system $A \otimes B$ the functor maps morphisms this way $F : f \otimes I \to I \otimes g$...I think. I haven't figured that out yet.
Feb
25
comment Examples of colimits in a category of categories
Thanks Zhen, but isn't that just in the category of sets? In the question, I mean in a category of categories.
Feb
25
comment Are these endofunctor categories compactly accessible? (Given a suitable base…)
Thank you for your help here. For the base category, I am thinking of the subcategory of CHU as defined here in section 3.4. Do we still end up in the situation where all functors of the above defined type are just the identity?
Feb
25
comment Are these endofunctor categories compactly accessible? (Given a suitable base…)
I don't see how this could be the identity. If the functor mapped all endomorphisms on $O$ to the identity morphism on $O$, that doesn't seem like an identity functor. What am I missing here? I have a question about how we can have lots of structure in our endofunctor category. Would you be able to look there and maybe answer how we can at least have a symmetric monoidal product?
Jun
9
comment Monoidal categories, but not in SET
Hi Julian, I'm afraid I cannot answer the question here. Qiaochu's post sounds like it might be an answer, but I would butcher it if I tried to write out an answer based on his suggestion.
Mar
12
comment Examples of abelian subgroups of non-abelian groups.
whoops, this is a copy of Brian's answer.
Jul
25
comment Kleisli category examples
I like how Qiaochu's comment got exactly 4 bumps. I would bump it too, but then it would b 5.
Jun
17
comment Monoidal categories, but not in SET
Hi, Qiaochu Yuan, I think maybe I do. I have visited this notion before. The category enriched over a monoidal category also sounds neat.