All Questions
Tagged with yoneda-lemma universal-property
3 questions
2
votes
1
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201
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Definition of the evaluation map as a universal element of a representation
This is exercise Exercise 2.3.iii from Riehl's "Category Theory in Context":
The set $B^A$ of functions from a set $A$ to a set $B$ represents the contravariant functor ${\rm Set}(-\times A,...
- 105
1
vote
1
answer
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Category theoretical proof that Abelianization commutes with products of group
Let $Grps$ and $Ab$ be the categories of groups and abelian groups respectively and lets denote $\times,\sqcup, \oplus$ the product and coproduct in Grps and the biproduct in $Ab$. If I want to prove ...
- 1,270
4
votes
1
answer
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Quotient of a free group on a set
Suppose I have a free group $F_S$ on a set $S,$ with a nonempty proper subset $T.$ If $N$ is the smallest normal subgroup of $F_S$ containing $T$, I would like to show that $F_S/N$ is also free. There'...
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