On homotopy types modelized by strict \infty-groupoids

zbMath1273.18030arXiv1206.2945MaRDI QIDQ2847372

Dimitri Ara

Publication date: 4 September 2013

Full work available at URL: https://arxiv.org/abs/1206.2945

zbMATH Keywords

homotopy categoryhomotopy typeEilenberg-Mac Lane spacechain complexstrict \(\infty\)-groupoid

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Classification of homotopy type (55P15) Homotopy groups, general; sets of homotopy classes (55Q05) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Chain complexes (category-theoretic aspects), dg categories (18G35) Chain complexes in algebraic topology (55U15) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40) Localization of categories, calculus of fractions (18E35) Homology of a product, Künneth formula (55U25)

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Strict \(\infty\)-groupoids are Grothendieck \(\infty\)-groupoids, A Quillen's Theorem A for strict \(\infty\)-categories. I: The simplicial proof, A Quillen Theorem B for strict ∞‐categories