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Tagged with yoneda-lemma monoidal-categories
4 questions
8
votes
1
answer
289
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generalized elements in monoidal categories
In a category $\mathcal{C}$, a generalized element of an object $A$ means a morphism to $A$. It follows from Yoneda lemma that the object $A$ is determined by the collection of generalized of elements ...
5
votes
1
answer
700
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Yoneda lemma for monoidal categories
I am looking at the Yoneda lemma trying to see where the assumption of "locally small" really comes in. Obviously in order to define a functor to the category sets using $Hom$-spaces we need ...
5
votes
0
answers
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Does Cantor Bernstein hold in a Closed Symmetric Monoidal Category?
In a closed symmetric monoidal category with $[I,X] \cong X$ for all $X$ is it true that having monomorphisms $m :A \rightarrow B$ and $m: B \rightarrow A$ is enough to imply $A \cong B$ ?
I tried to ...
8
votes
2
answers
1k
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Enrichments vs Internal homs
Consider the definition of existence internal homs for a general monoidal category category $\cal{C}$, mainly the existence of an adjoint for the functor
$$
X \otimes -: \cal{C} \to \cal{C},
$$
for ...