[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








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John R. Klein, Professor
Department of Mathematics
Wayne State University
Room 1213 FAB, 656 W. Kirby
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