Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steenrod coalgebras of simplicial complexes   In this paper, we extend earlier work by showing that if $X$ and $Y$ are
simplicial complexes (i.e. simplicial sets whose simplices are determined by
their vertices), a morphism $g:N(X)\to N(Y)$ of Steenrod coalgebras (normalized
chain-complexes equipped with extra structure) induces one of their topological
realizations $\hat{g}:|X|\to |Y|$. If $g$ is an isomorphism, then it induces an
isomorphism between $X$ and $Y$, implying that they are homeomorphic.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an