Aitchison, I., The geometry of oriented cubes, unpublished manuscript. Home/Search Document Not in Database Summary Related Articles Check |
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Pasting Diagrams in n-Categories with Applications to Coherence.. - Johnson (1987) (1 citation) (Correct)
....of the free n category on the n simplex was begun by Roberts [18] Street and Duskin worked on the problem for a number of years and recently Street [20] has obtained a solution. Walters has argued that there should be a more geometric description of such a geometric construction and Aitchison [1] has analysed the geometry of the free n category on the n cube , but his work did not achieve Walters hoped for simplification of Street s results. The relationship between orientals and higher coherence conditions has been particularly tantalizing. Mac Lane proved the first coherence theorems ....
....from the normal description is not necessary to obtain the results below, but it does simplify the treatment because all the pasting schemes we use can be made into labelled well formed simplicial sets. Let T be the pasting scheme given by T 0 = 33 T 1 = f(m; n; a) m;n 2 , m n, a 2 [1]g T 2 = f(l; m; n; a; b) l; m;n 2 , l m n, a; b 2 [1]g and with B 1 (l; m; n; a; b) f(l; m; a) m; n; b)g B 0 (l; m; n; a; b) fmg E 1 (l; m; n; a; b) f(l; n; 1)g E 0 (l; m; n; a; b) B 0 (m; n; a) fmg E 0 (m; n; a) fng For example: R(l; m; n; 0; 1) m l n Gamma ....
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Aitchison, I., The geometry of oriented cubes, unpublished manuscript.
Homotopy Invariants of Multiple Categories and Concurrency in.. - Gaucher (1999) (Correct)
.... ) Phi(ffi ( Gamma) 1 1 (0 n 1 ) ffi ( Gamma) n 2 n 2 (0 n 1 ) Y 1 ; Y h ) where Y 1 , Y h are morphisms of I n 2 of dimension less than or equal to n and where Phi is a function which only uses compositions (we can in fact find an explicit expression of Phi in (Aitchison, 1986)) Because of h being an functor, we have h(s n 1 (R(0n 2 ) Phi(h(ffi ( Gamma) 1 1 (0 n 1 ) h(ffi ( Gamma) n 2 n 2 (0 n 1 ) h(Y 1 ) h(Y h ) There is only one argument of dimension n 1, the other ones being of dimension strictly less than n 1. So h(s n 1 ....
Aitchison, I. R. (1986). The geometry of oriented cubes. Macquarie Mathematics Reports 86-0082.
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