[ALGTOP-L] From simplicial to cosimplicial objects
John R. Klein
nielkj at gmail.com
Tue Oct 7 12:11:06 EDT 2008
Suppose D is the category of finite ordered sets and D^o is its opposite.
It has occurred to me that there is an embedding D --> D^o which maps
[n] ---> [n+1]
(where [n] = {0 < 1 < 2 ... < n}), where the
i-th degeneracy
s_i : [n] ---> [n-1] (0 \le i \le n-1)
maps to the (i+1)-st face
d_{i+1} : [n] --> [n+1]
the ith face d_i:[n] --> [n+1] maps to s_i: [n+2] --> [n+1]
My question: is this known? (and is it correct?)
(If it's correct, then it gives a way of producing cosimplicial
objects from simplicial ones.)
jk
--
John R. Klein, Professor
Department of Mathematics
Wayne State University
Room 1213 FAB, 656 W. Kirby
Detroit, MI 48202
voice: (313) 577-3174
fax: (313) 577-7596
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