caa a22 4500 445378727 CHVBK 20180317143011.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-008-9174-z doi (NATIONALLICENCE)springer-10.1007/s10485-008-9174-z A Coherent Homotopy Category of 2-track Commutative Cubes [Elektronische Daten] [K. Hardie, K. Kamps, P. Witbooi] We consider a category ${\mathcal H}^{\ominus \otimes}$ (the homotopy category of homotopy squares) whose objects are homotopy commutative squares of spaces and whose morphisms are cubical diagrams subject to a coherent homotopy relation. The main result characterises the isomorphisms of ${\mathcal H}^{\ominus \otimes}$ to be the cube morphisms whose forward arrows are homotopy equivalences. As a first application of the new category we give a direct 2-track theoretic definition of the quaternary Toda bracket operation. Springer Science+Business Media B.V., 2008 Track nationallicence Semitrack nationallicence Homotopy 2-groupoid nationallicence Triple category nationallicence Homotopy pair nationallicence Interchange 2-track nationallicence Toda bracket nationallicence Hardie K. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, Cape Town, Republic of South Africa aut Kamps K. Fernuniversität, 58084, Hagen, Germany aut Witbooi P. Department of Mathematics, University of the Western Cape, 7535, Bellville, Republic of South Africa aut Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 39-60 0927-2852 19:1<39 2011 19 10485 https://doi.org/10.1007/s10485-008-9174-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-008-9174-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hardie K. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, Cape Town, Republic of South Africa aut NATIONALLICENCE 700 1- Kamps K. Fernuniversität, 58084, Hagen, Germany aut NATIONALLICENCE 700 1- Witbooi P. Department of Mathematics, University of the Western Cape, 7535, Bellville, Republic of South Africa aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 39-60 0927-2852 19:1<39 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer