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- Simplicial_presheaf abstract "In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the category of presheaves on a site. The notion was introduced by A. Joyal in 1970s. Similarly, a simplicial sheaf on a site is a simplicial object in the category of sheaves on the site.Example: Let us consider, say, the étale site of a scheme S. Each U in the site represents the presheaf . Thus, a simplicial scheme, a simplicial object in the site, represents a simplicial presheaf (in fact, often a simplicial sheaf).Example: Let G be a presheaf of groupoids. Then taking nerves section-wise, one obtains a simplicial presheaf . For example, one might set . These types of examples appear in K-theory.If is a local weak equivalence of simplicial presheaves, then the induced map is also a local weak equivalence.".
- Simplicial_presheaf wikiPageExternalLink simplicial-presheaves-model.
- Simplicial_presheaf wikiPageExternalLink crm-2008.pdf.
- Simplicial_presheaf wikiPageExternalLink ~jardine.
- Simplicial_presheaf wikiPageExternalLink Fields-01.pdf.
- Simplicial_presheaf wikiPageID "39611193".
- Simplicial_presheaf wikiPageRevisionID "587831787".
- Simplicial_presheaf subject Category:Functors.
- Simplicial_presheaf subject Category:Homotopy_theory.
- Simplicial_presheaf subject Category:Simplicial_sets.
- Simplicial_presheaf comment "In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the category of presheaves on a site. The notion was introduced by A. Joyal in 1970s.".
- Simplicial_presheaf label "Simplicial presheaf".
- Simplicial_presheaf sameAs m.0vxfrc3.
- Simplicial_presheaf sameAs Q17103298.
- Simplicial_presheaf sameAs Q17103298.
- Simplicial_presheaf wasDerivedFrom Simplicial_presheaf?oldid=587831787.
- Simplicial_presheaf isPrimaryTopicOf Simplicial_presheaf.