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(-,U)} . Thus, a simplicial scheme, a simplicial object in the site, represents a simplicial presheaf (in fact, often a simplicial sheaf). Example: Let...

n ) n ≥ 0 {\displaystyle (U_{n})_{n\geq 0}} instead of the above simplicial scheme determined by a usual étale cover. Taking finer and finer hypercoverings...

for schemes", Astérisque: 99–201, arXiv:1309.1198, Bibcode:2013arXiv1309.1198B, MR 3379634 Friedlander, Eric M. (1982), Étale homotopy of simplicial schemes...

study of the pro-simplicial set associated to the étale topos of a scheme is called étale homotopy theory. In good cases (if the scheme is Noetherian and...

the category of simplicial objects on S h v ( S m S ) N i s {\displaystyle Shv(Sm_{S})_{Nis}} . Such an object is also called a simplicial sheaf on S m S...

differential graded algebras (over Q {\displaystyle \mathbb {Q} } ), simplicial commutative rings or E ∞ {\displaystyle E_{\infty }} -ring spectra from...

simplicial rings, or commutative ring spectra. From the functor of points point-of-view, a derived scheme is a sheaf X on the category of simplicial commutative...

together" simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the...

and in particular homotopy theory, a hypercovering (or hypercover) is a simplicial object that generalises the Čech nerve of a cover. For the Čech nerve...

pro-simplicial set is an inverse system of simplicial sets. A pro-simplicial set is called pro-finite if each term of the inverse system of simplicial sets...

Deligne–Mumford stack. Conversely, any DM stack is of this form. Simplicial scheme Algebraic stacks, Ch 3. § 1. Gillet 1984. Behrend, Kai; Conrad, Brian;...

into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh...

algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object in the...

model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure). It is an ∞-category generalization...

topological simplices as prescribed by the simplicial set structure of X. Orbifold fundamental group Fundamental group scheme Poincaré, Henri (1895). "Analysis...

of Algebraic Varieties, memoir of the AMS, 1994 Etale Homotopy of Simplicial Schemes, Annals of mathematical studies, Princeton University Press 1982 Editor...

Abstract homotopical model for topological spaces Simplicial set Kan complex – Map between simplicial sets with lifting propertyPages displaying short...

An implementation typically involves four steps: coordinate skewing, simplicial subdivision, gradient selection, and kernel summation. An input coordinate...

definition of a spectrum. A simplicial set is not thought of as a space; i.e., we generally distinguish between simplicial sets and their geometric realizations...

abstract simplicial complexes. One of the assumptions is a non-triviality condition: If the building is an n‑dimensional abstract simplicial complex,...