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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.

**3**

votes

**1**answer

Since about the time I asked the question, What is the precise relationship between "prodsimplicial sets" and rooted trees? I have been playing with these rooted trees and their correspondence to cert …

asked Sep 6 '12 by Spice the Bird

**2**

votes

Here I will sketch a proof, leaving many of the details out. The proof will be by induction on the number of edges of the rooted tree, which is the same as the dimension of the PS-complex (prod-simpli …

answered Nov 16 '12 by Spice the Bird

**1**

vote

Any time you have a topological groupoid, you have a simplicial groupoid since geometric realization preserves finite limits. Although this seems like a rather trivial remark this allows for one to st …

answered Dec 26 '11 by Spice the Bird

**3**

votes

**1**answer

Let us first remark that all of this takes place on the boundary of $\Delta^n$. The question that I wanted to solve that led to the question in the title is as follows: Let $f:\Delta^{n-1}\hookrightar …

asked Jan 29 '12 by Spice the Bird

**19**

votes

**2**answers

We have a characterization when we want $|X|$ to be a PL-manifold, in particular that the links of all the vertices are themselves (PL) spheres. If we are in the category of PL- spaces then this is a …

asked Dec 13 '12 by Spice the Bird

**11**

votes

**1**answer

In Keven Walker's answer to the question, Cubical vs. simplicial singular homology it is written:
Personally, I think it is more convenient to do singular homology with the larger collection …

asked May 23 '12 by Spice the Bird