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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.
Jun
17
comment Monoidal categories, but not in SET
Hi Martin, The only monoidal structure I want to capture is the kind of structure we find in the wikipedia entry on "Monoidal Category". I want to present a category where I can tensor objects and then tensor morphisms to map products to products. I think the real problem is that it will be hard to present a category without sets, but that is the challenge.
Jun
5
comment All about (co)algebras for the identity functor
I gave it the check. Thanks again.
Jun
4
comment All about (co)algebras for the identity functor
Does anyone want to say definitively that there are no interesting (co)monads based on identity functor?
Jun
3
comment All about (co)algebras for the identity functor
Hey, I can't vote your answer up yet as i have no reputation points. In lieu of that: Thanks!