The groupoidal analogue \(\widetilde{{\Theta}}\) to Joyal's category \(\Theta\) is a test category

DOI10.1007/s10485-011-9255-2zbMath1434.18009arXiv1012.4319OpenAlexW3100814223MaRDI QIDQ1928247

Dimitri Ara

Publication date: 2 January 2013

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4319

zbMATH Keywords

localizationhomotopyweak equivalence\(\infty\)-category\(\infty\)-groupoidtest categorycell categorydécalageglobular extension

Mathematics Subject Classification ID

Classification of homotopy type (55P15) Localization and completion in homotopy theory (55P60) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Localization of categories, calculus of fractions (18E35) Topological categories, foundations of homotopy theory (55U40) Homotopical algebra, Quillen model categories, derivators (18N40) 2-categories, bicategories, double categories (18N10) ((infty,1))-categories (quasi-categories, Segal spaces, etc.); (infty)-topoi, stable (infty)-categories (18N60)

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Cites Work

• The Brown-Golasiński model structure on strict \(\infty \)-groupoids revisited
• Joyal's category \(\varTheta\) is a test category
• A cellular nerve for higher categories
• Monoidal globular categories as a natural environment for the theory of weak \(n\)-categories
• The universal property of the multitude of trees
• Iterated wreath product of the simplex category and iterated loop spaces
• Complexe cotangent et déformations. II
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