Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stable cooperations of Morava K-Theory and the fiber product of
  automorphism groups of formal group laws   The Hopf algebra $K(n)_*(K(n))$, the stable cooperations of Morava $K$-theory
at an odd prime, is well-known. Whereas the main part of $K(n)_*(K(n))$
corepresents the group-valued functor consisting of the automorphisms of a
formal group law of height $n$, relations between the whole structure of
$K(n)_*(K(n))$ and formal group laws have not been investigated well. Firstly,
we constitute the fiber product of two natural transformations between the
automorphism groups of formal group laws, and the corepresenting Hopf algebra
$C_*$. Next, we construct a Hopf algebra homomorphism from $C_*$ to
$K(n)_*(K(n))$ via Boardman's stable comodule algebras. By Yagita's results and
the algebra structure of $K(n)_*(K(n))$, we see that the homomorphism is an
isomorphism. The isomorphism clarifies the relationship between the Hopf
algebra structure of $K(n)_*(K(n))$ including the exterior algebra part and
formal group laws.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga