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Notice added Authoritative reference needed by Paris
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Paris
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Paris
Paris
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pair of injective morphismmorphisms of contractible simplicial setsgroups

Let $X$ and $Y$ be two Kan complexessimplicial groups such that there exists $f:X\rightarrow Y$ and $g:Y\rightarrow X $ two injective simplicial morphisms of simplicial groups. Suppose that $X$ is contractible, does it follow that $Y$ is contractible ?

pair of injective morphism of contractible simplicial sets

Let $X$ and $Y$ be two Kan complexes such that there exists $f:X\rightarrow Y$ and $g:Y\rightarrow X $ two injective simplicial morphisms. Suppose that $X$ is contractible, does it follow that $Y$ is contractible ?

pair of injective morphisms of simplicial groups

Let $X$ and $Y$ be two simplicial groups such that there exists $f:X\rightarrow Y$ and $g:Y\rightarrow X $ two injective morphisms of simplicial groups. Suppose that $X$ is contractible, does it follow that $Y$ is contractible ?

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Paris
Paris
  • 717
  • 3
  • 13

pair of injective morphism of contractible simplicial sets

Let $X$ and $Y$ be two Kan complexes such that there exists $f:X\rightarrow Y$ and $g:Y\rightarrow X $ two injective simplicial morphisms. Suppose that $X$ is contractible, does it follow that $Y$ is contractible ?