All Questions
Tagged with locally-presentable-categories reference-request
8 questions
15
votes
2
answers
754
views
$\mu$-presentable object as $\mu$-small colimit of $\lambda$-presentable objects
Remark 1.30 of Adámek and Rosický, Locally Presentable and Accessible Categories claims that in any locally $\lambda$-presentable category, each $\mu$-presentable object (for $\mu\ge\lambda$) can be ...
- 25.2k
13
votes
1
answer
474
views
Is there any references on the tensor product of presentable (1-)categories?
Is there any references on the tensor product of (locally) presentable categories ?
All I know about this is Lurie's book that deals with the $\infty$-categorical version, and a few references that ...
- 42.4k
9
votes
3
answers
914
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Enriched locally presentable categories
Is there a standard reference for the theory (if it exists) of $\mathcal{V}$-enriched locally presentable categories? Here $\mathcal{V}$ is a cosmos. Does anything unexpected happens here in contrast ...
- 63.1k
9
votes
1
answer
478
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From Topoi to Grothendieck categories
This question is mostly about a reference request. Let $\mathcal{E}$ be a Grothendieck topos. I am looking for a reference of the following two facts. I am aware that $(2) \Rightarrow (1)$ by Gabriel-...
- 9,111
8
votes
1
answer
253
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Compact objects in slice categories of finitely presentable categories
Given a locally finitely presentable category $\mathscr C$ and an object $X \in \mathscr C$, it is not so hard to show that a morphism $(X \to Y)$ is compact in $\mathscr C_{X/}$ if it can be obtained ...
- 28.7k
5
votes
0
answers
255
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Is the category of topologically free $k[[h]]$-modules locally presentable?
$\newcommand{\colim}{\operatorname{colim}}$
Let $k$ be a field (of characteristic 0, say) and $M$ be a module over $R=k[[h]]$. Recall that the $h$-adic completion of $M$ is
$$
\hat M:=\lim M/h^nM,
$$
...
- 8,524
4
votes
1
answer
362
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Locally presentable categories
Under category
Let $C$ be a locally presentable category, and let $c$ be an object of $C$. Lets denote by $C^{/c}$ the under category, objects are maps $c\rightarrow x$ and morphisms are the evident ...
- 511
4
votes
1
answer
339
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Coreflective subcategories in Grothendieck/locally presentable categories
This question is a reference request for the following result or two results, which I believe are rather easy to prove.
Lemma. Let $\mathcal K$ be a locally presentable category and $\mathcal A\...
- 15.6k