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37 Some $n$-category definitions model $k$-morphisms on the standard bihedron (interval, bigon, ...). |
37 Some $n$-category definitions model $k$-morphisms on the standard bihedron (interval, bigon, ...). |
38 Other definitions have a separate set of 1-morphisms for each interval $[0,l] \sub \r$, |
38 Other definitions have a separate set of 1-morphisms for each interval $[0,l] \sub \r$, |
39 a separate set of 2-morphisms for each rectangle $[0,l_1]\times [0,l_2] \sub \r^2$, |
39 a separate set of 2-morphisms for each rectangle $[0,l_1]\times [0,l_2] \sub \r^2$, |
40 and so on. |
40 and so on. |
41 (This allows for strict associativity.) |
41 (This allows for strict associativity.) |
42 Still other definitions \nn{need refs for all these; maybe the Leinster book} |
42 Still other definitions \nn{need refs for all these; maybe the Leinster book \cite{MR2094071}} |
43 model the $k$-morphisms on more complicated combinatorial polyhedra. |
43 model the $k$-morphisms on more complicated combinatorial polyhedra. |
44 |
44 |
45 We will allow our $k$-morphisms to have any shape, so long as it is homeomorphic to |
45 We will allow our $k$-morphisms to have any shape, so long as it is homeomorphic to |
46 the standard $k$-ball. |
46 the standard $k$-ball. |
47 In other words, |
47 In other words, |