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Results tagged with simplicial-stuff
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user 419447
For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
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Is the (inverse) Dold-Kan functor fully faithful on chain complexes of commutative monoids?
My question
The background/notation for all of the content of this post is in Lurie, Higher Algebra [HA], Ch. 1.2.3. Everything is purely 1-categorical.
Let $\mathcal{A}$ a semiadditive category (with …
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Accepted
Is the (inverse) Dold-Kan functor fully faithful on chain complexes of commutative monoids?
Thanks everyone, for completeness I'll outline the proof here. The answer is yes, over $\mathbf{CMon}$, $\mathrm{DK}$ is fully faithful. To check this we define $N_*$ in the opposite direction taking …