Clemens Berger, A Cellular Nerve for Higher Categories (Rev #2)

1. Globular theories and cellular nerves


Batanin’s ω\omega-operads are described by their operator categories which are called globular theories.

Definition (finite planar level tree)

A finite planar level tree ( or for short just a tree) is a graded set (T(n)) nmathhbN 0(T(n))_{n\in \mathhb{N}_0} endowed with a map i T:T >0i_T: T_{\gt 0} decreasing the degree by one and such that all fibers i T 1(x)i_T^{-1}(x) are linearly ordered.

Lemma and Definition (ω\omega-graph of sectors of a tree)

Let TT be a tree.

A TT-sector of height kk is defined to be a cospan

y y y\array{ y^\prime&y^{\prime\prime} \\ \searrow&\swarrow \\ &y }

Revision on November 18, 2012 at 14:23:00 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.