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Longer titles found: Pro-simplicial set (view), Opposite simplicial set (view), Subdivision (simplicial set) (view), Extension (simplicial set) (view), Join (simplicial sets) (view), Twisted diagonal (simplicial sets) (view), Weak equivalence between simplicial sets (view), Fibration of simplicial sets (view), Bisimplicial set (view)

searching for Simplicial set 6 found (69 total)

alternate case: simplicial set

Hypercovering (575 words) [view diff] exact match in snippet view article find links to article

the cover is contractible, then one can contract these sets and get a simplicial set that is weakly equivalent to X {\displaystyle X} in a natural way. For

Joyal's theta category (160 words) [view diff] exact match in snippet view article find links to article

(which is the standard definition today), an ∞-category is defined as a simplicial set satisfying the weak Kan condition. In a similar way, Joyal proposed

Category of elements (2,810 words) [view diff] exact match in snippet view article find links to article

as Lawvere's concept of hyperdoctrine. The category of elements of a simplicial set is fundamental in simplicial homotopy theory, a branch of algebraic

Limits and colimits in an ∞-category (225 words) [view diff] exact match in snippet view article find links to article

conditions) in higher category theory. Let I {\displaystyle I} be a simplicial set and C {\displaystyle C} an ∞-category (a weak Kan complex). Fix a Grothendieck

2-category (2,524 words) [view diff] exact match in snippet view article find links to article

nerve N h c ( C ) {\displaystyle N^{hc}(C)} of a 2-category C is a simplicial set where each n-simplex is determined by the following data: n objects

Hodge structure (4,881 words) [view diff] exact match in snippet view article find links to article

structures. The E1-page has explicit terms with a differential coming from a simplicial set. Any smooth variety X admits a smooth compactification with complement