R. Brown and P. J. Higgins. Tensor products and homotopies for !- groupoids and crossed complexes. J. Pure and Appl. Algebra 47 (1987), 1--33 Home/Search Document Not in Database Summary Related Articles Check |
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On the Twisted Cobar Construction - Baues, Tonks (1997) (1 citation) (Correct)
....construction. 1 2 Hans Baues and Andrew Tonks The proof of the main theorem relies on the geometric cobar construction introduced in [2] and the computation of its crossed chain complex. The theory of crossed chain complexes goes back to Whitehead [24] and has been developed in, for example, [5, 11, 13]. Here we also need the associated theory of crossed chain algebras [8, 23] first examples of such algebras were studied in [5, 6, 7, 10, 22] For the convenience of the reader and to make the main results completely accessible we give in the first part all relevant definitions and facts. The ....
....by the relation that F G if there is a natural transformation F G in Mon 0 which for each object is a homotopy equivalence in the category of pointed topological spaces. The crossed cobar construction Let C be the category Crs of crossed complexes (see for example the work of Brown Higgins [11, 12, 13, 14, 15]) This is a monoidal closed category which shares many of the nice properties of the category of chain complexes, but with some non abelian features in low dimensions. Recall that the tensor product of crossed complexes is defined via an equivalence with the category of groupoids in [11] the ....
R. Brown and P. J. Higgins. Tensor products and homotopies for !- groupoids and crossed complexes. J. Pure and Appl. Algebra 47 (1987), 1--33
On the Twisted Cobar Construction - Baues, Tonks (1997) (1 citation) (Correct)
....construction. 1 2 Hans Baues and Andrew Tonks The proof of the main theorem relies on the geometric cobar construction introduced in [2] and the computation of its crossed chain complex. The theory of crossed chain complexes goes back to Whitehead [24] and has been developed in, for example, [5, 11, 13]. Here we also need the associated theory of crossed chain algebras [8, 23] first examples of such algebras were studied in [5, 6, 7, 10, 22] For the convenience of the reader and to make the main results completely accessible we give in the first part all relevant definitions and facts. The ....
....by the relation that F G if there is a natural transformation F G in Mon 0 which for each object is a homotopy equivalence in the category of pointed topological spaces. The crossed cobar construction Let C be the category Crs of crossed complexes (see for example the work of Brown Higgins [11, 12, 13, 14, 15]) This is a monoidal closed category which shares many of the nice properties of the category of chain complexes, but with some non abelian features in low dimensions. Recall that the tensor product of crossed complexes is defined via an equivalence with the category of groupoids in [11] the ....
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R. Brown and P. J. Higgins. The algebra of cubes. J. Pure and Appl. Algebra 21 (1981), 233--260
Theory and Applications of Crossed Complexes - Tonks (1993) (2 citations) (Correct)
.... The total crossed complex D of a double crossed complex C is essentially that given by generators c i;j 2 D n for all elements of C i;j with i j = n, subject to certain geometrical relations which are similar to those in the Brown Higgins definition of the tensor product of crossed complexes [12]. In fact our definition is constructed so that given a pair of crossed complexes A, B there is an obvious double crossed complex whose total crossed complex is the tensor product A Omega B. We also define a total functor from the category of simplicial crossed complexes. In chapter 2 the ....
....ffi 2 c 0 i;j = c i;j ffi c 0 i;j for i = 0 or j 2 1.2. 3 Tensor products and double complexes In this section we will consider a functor Crs Theta Crs Omega (2) Crs (2) whose composite with the functor Tot defined above gives the tensor product of crossed complexes as defined in [12]. 16 Definition 1.2.3 Suppose C, D are crossed complexes. Then the double crossed complex C Omega (2) D is defined as follows ffl Each set (C Omega (2) D) i;j is given by the cartesian product C i Theta D j . Elements (c; d) will be written c Omega d. ffl The horizontal crossed ....
[Article contains additional citation context not shown here]
R. Brown and P. J. Higgins. Tensor products and homotopies for !-groupoids and crossed complexes. J. Pure and Appl. Algebra 47 (1987), 1--33
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