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 Curious
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Mar
7
awarded  Curious
Mar
4
awarded  Tumbleweed
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
awarded  Commentator
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
asked Examples of colimits in a category of categories
Feb
25
revised Categorical presentation of “the theory of structure in Set”
added 367 characters in body
Feb
25
asked Categorical presentation of “the theory of structure in Set”
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?
Feb
23
asked Are these endofunctor categories compactly accessible? (Given a suitable base…)
Jan
2
accepted Compact objects and locally finitely presentable categories (the Category of Groups)
Jan
2
revised Compact objects and locally finitely presentable categories (the Category of Groups)
added 160 characters in body
Jan
2
asked Compact objects and locally finitely presentable categories (the Category of Groups)
Sep
24
awarded  Autobiographer
Sep
1
awarded  Editor
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.