Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steenrod coalgebras III. The fundamental group   In this note, we extend earlier work by showing that if $X$ and $Y$ are
delta-complexes (i.e. simplicial sets without degeneracy operators), a morphism
$g:N(X)\to N(Y)$ of Steenrod coalgebras (normalized chain-complexes equipped
with extra structure) induces one of 2-skeleta $\hat{g}:X_{2}\to Y_{2}$,
inducing a homomorphism $\pi_{1}(\hat{g}):\pi_{1}(X)\to\pi_{1}(Y)$ that is an
isomorphism if $g$ is an isomorphism. This implies a corresponding conclusion
for a morphism $g:C(X)\to C(Y)$ of Steenrod coalgebras on unnormalized
chain-complexes of simplicial sets.

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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th