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searching for Simplex category 4 found (106 total)

Density theorem (category theory) (798 words) [view diff] exact match in snippet view article

For example, by definition, a simplicial set is a presheaf on the simplex category Δ and a representable simplicial set is exactly of the form Δ n = Hom

Opposite simplicial set (387 words) [view diff] exact match in snippet view article find links to article

Both correspond to each other under the nerve construction. On the simplex category Δ {\displaystyle \Delta } , there is an automorphism ρ : Δ → Δ {\displaystyle

Pursuing Stacks (894 words) [view diff] exact match in snippet view article find links to article

to “homotopy-theoretic”?, Mathoverflow.net What's special about the Simplex category? R. Brown, The Origins of `Pursuing Stacks' by Alexander Grothendieck

Limits and colimits in an ∞-category (393 words) [view diff] exact match in snippet view article find links to article

a} . A typical case is when I = Δ {\displaystyle I=\Delta } is the simplex category or rather its opposite; in the latter case, the functor f {\displaystyle