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Homotopical Algebraic Geometry I: Topos theory
, 2002
"... This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher topos. For this, we use Scategories (i.e. simplicially enriched categories) as models for certain kind of ..."
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Cited by 32 (20 self)
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This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher topos. For this, we use Scategories (i.e. simplicially enriched categories) as models for certain kind of ∞categories, and we develop the notions of Stopologies, Ssites and stacks over them. We prove in particular, that for an Scategory T endowed with an Stopology, there exists a model
Operads In HigherDimensional Category Theory
, 2004
"... The purpose of this paper is to set up a theory of generalized operads and multicategories and to use it as a language in which to propose a definition of weak ncategory. Included is a full explanation of why the proposed definition of ncategory is a reasonable one, and of what happens when n <= 2 ..."
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Cited by 32 (2 self)
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The purpose of this paper is to set up a theory of generalized operads and multicategories and to use it as a language in which to propose a definition of weak ncategory. Included is a full explanation of why the proposed definition of ncategory is a reasonable one, and of what happens when n <= 2. Generalized operads and multicategories play other parts in higherdimensional algebra too, some of which are outlined here: for instance, they can be used to simplify the opetopic approach to ncategories expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.
SIMPLICIAL LOCALIZATION OF MONOIDAL STRUCTURES, AND A NONLINEAR VERSION OF DELIGNE’S CONJECTURE JOACHIM KOCK AND BERTRAND TO ËN
, 2003
"... is a (weak) 2monoid in sSet. This applies in particular when M is the category of Abimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2monoid. Deligne’s conjecture. Deligne’s conjecture (stated informally ..."
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is a (weak) 2monoid in sSet. This applies in particular when M is the category of Abimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2monoid. Deligne’s conjecture. Deligne’s conjecture (stated informally in a letter in 1993) states that the Hochschild cohomology HH(A) of an associative algebra A is a 2algebra — this means that up to homotopy it has two compatible multiplication laws.
SIMPLICIAL LOCALIZATION OF MONOIDAL STRUCTURES, AND A NONLINEAR VERSION OF DELIGNE’S CONJECTURE JOACHIM KOCK AND BERTRAND TO ËN
, 2003
"... is a (weak) 2monoid in sSet. This applies in particular when M is the category of Abimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2monoid. Deligne’s conjecture. Deligne’s conjecture (stated informally ..."
Abstract
 Add to MetaCart
is a (weak) 2monoid in sSet. This applies in particular when M is the category of Abimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2monoid. Deligne’s conjecture. Deligne’s conjecture (stated informally in a letter in 1993) states that the Hochschild cohomology HH(A) of an associative algebra A is a 2algebra — this means that up to homotopy it has two compatible multiplication laws.