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Results tagged with yoneda-lemma
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user 124549
3
votes
Is Cauchy completion the largest extension with the same free cocompletion?
The answer is positive.
I found a published account with details to be chapter 6 and 7 of Handbook of Categorical Algebra 1 by Francis Borceux.
Thanks to the comments, useful links that summarize how …
- 5,230
5
votes
1
answer
316
views
Is Cauchy completion the largest extension with the same free cocompletion?
EDIT Title has been edited.
Let $C$ be a category, and $$\hat{C} = [C^{op}, (Set)]$$ be its free cocompletion. Despite its name, the free cocompletion of free cocompletion is not equivalent to the fr …
- 5,230
3
votes
0
answers
266
views
All functors "are" left adjoints, and applications?
Throughout this thread, let us assume smallness.
All functors "are" left adjoints
Let $D \xrightarrow{F} C$ be any functor, which induces
$$ D \xrightarrow{F} \hat{C}$$
by compositing the Yoneda embed …
- 5,230