# Tagged Questions

**8**

votes

**1**answer

299 views

### Question about tetrahedron decomposition

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrahedron for which this ...

**1**

vote

**1**answer

166 views

### How to call a simplicial set where every boundary of a simplex can be filled?

What is the correct terminology for the following property of a simplicial set $X_\bullet$:
For every $k\geq 0$, every map $\partial\Delta^k\to X_\bullet$ can be extended to a map $\Delta^k\to ...

**6**

votes

**0**answers

448 views

### Historical and terminological questions about Dan Kan's Ex functor and its relation to the classical case of simplicial complexes

Recall that we may define a functor $\xi:\Delta\to \operatorname{Poset}$ sending a simplex $[n]$ to the set of monotone injections $[k]\hookrightarrow [n]$ for $k\geq 0$ (effectively, $k\leq n$ as ...