Brown, Ronald; Higgins, Philip J. The equivalence of infinity-groupoids and crossed complexes. (English) Zbl 0487.55007 Cah. Topol. Géom. Différ. 22, 371-386 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 28 Documents MSC: 55U35 Abstract and axiomatic homotopy theory in algebraic topology 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) 57M05 Fundamental group, presentations, free differential calculus 18G55 Nonabelian homotopical algebra (MSC2010) 55U05 Abstract complexes in algebraic topology Keywords:n-fold categories; equivalence of categories; infinity-groupoids; crossed complexes; omega-groupoids Citations:Zbl 0475.55009; Zbl 0468.55007 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] 1 R. Brown & P.J. Higgins , On the algebra of cubes, J. Pure & Appl . Algebra , 21 ( 1981 ), 233 - 260 . MR 617135 | Zbl 0468.55007 · Zbl 0468.55007 · doi:10.1016/0022-4049(81)90018-9 [2] 2 R. Brown & P.J. Higgins , Colimit theorems for relative homotopy groups, J. Pure & Appl . Algebra 22 ( 1981 ), 11 - 41 . MR 621285 | Zbl 0475.55009 · Zbl 0475.55009 · doi:10.1016/0022-4049(81)90080-3 [3] 3 R. Brown & P.J. Higgins , The equivalence of \omega -groupoids and cubical T-complexe s , This issue. · Zbl 0486.55011 [4] 4 R. Brown & C.B. Spencer , G-groupoids, crossed modules and the fundamental groupoid of a topological group , Proc. Kon. Akad. v. Wet. 79 ( 1976 ), 296 . MR 419643 | Zbl 0333.55011 · Zbl 0333.55011 [5] 5 R. Brown & C.B. Spencer , Double groupoids and crossed modules , Cahiers Top. et Géom. Diff. XVII - 4 ( 1976 ), 343 - 362 . Numdam | MR 440553 | Zbl 0344.18004 · Zbl 0344.18004 [6] 6 M.K. Dakin , Kan complexes and multiple groupoid structures , Ph. D. Thesis University of Wale s , 1977 . MR 766238 · Zbl 0566.55010 [7] 7 A. Dold , Homology of symmetric products and other functors of complexes , Ann. of Math. 68 ( 1958 ), 54 - 80 . MR 97057 | Zbl 0082.37701 · Zbl 0082.37701 · doi:10.2307/1970043 [8] 8 A. & C. Ehresmann , Multiple functors II, III , Cahiers Top. et Géom. Diff. xx ( 1978 ), 295 - 333 , 387 - 443 . Numdam | Zbl 0415.18006 · Zbl 0415.18006 [9] 9 D.M. Kan , Functors involving c.s.s. complexes , Trans. A.M.S. 87 ( 1958 ), 330 . MR 131873 | Zbl 0090.39001 · Zbl 0090.39001 · doi:10.2307/1993103 [10] 10 C.B. Sp Encer , An abstract setting for homotopy pushouts and pullbacks , Cahiers Top. et Géom. Diff. XVIII- 4 ( 1977 ), 409 - 430 . Numdam | MR 486054 | Zbl 0378.18008 · Zbl 0378.18008 [11] 11 O. Wyler , Multiple functor categories , Mimeographed Note s, Camegie-Mellon University , 1972 . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.