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Results tagged with accessible-categories
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user 104432
13
votes
Non-small objects in categories
In the category $\mathsf{Top}$ of topological spaces and continuous maps the only $\lambda$-presentable objects are discrete spaces. This appears 1.14(6) in Locally presentable and Accessible categori …
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10
votes
Accepted
Can the dual of a finitely-accessible category be accessible?
In Accessible Categories: The Foundations of Categorical Model Theory by Makkai and Paré, there is the example of a finitely accessible self-dual category. Apparently the example is due to Isbell. Thi …
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7
votes
Example: Accessible category without colimits
The category Hil of Hilbert spaces, considered as a full subcategory of Ban is $\aleph_1$-accessible but not locally presentable, in fact it is self dual.
The category Lin of linear orders and strict …
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4
votes
Relation between Ind-completion and "additive"-ind-completion
Let $\mathcal{V}$ be a cocomplete monoidal category which can be presented by a limit theory, so that $\mathcal{V} = \mathsf{Lex}(\mathbb{T},\text{Set})$, of course this is the case of your question.
…
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4
votes
Is every accessible category well-powered?
Some considerations, not a full answer (yet).
In Accessible categories and models for linear logic, at page 2, Barr claims that every accessible category is well powered. He even claims that is obse …
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3
votes
Which abelian groups are $\aleph_1$-filtered colimits of finitely-generated abelian groups?
Ycor answered the question, so I shall add a couple of remarks providing some insight about why these results should be true at all.
Ind-completions are nested $$\text{Ind}(C) \supset \text{Ind}_{\ale …
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2
votes
What are the reflective subcategories of the category of presentable categories?
The following is a very long comment and works in $1$-category theory.
I claim that you can characterize very well coreflective subcategories.
My strategy works even for reflective.
There is a …
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