Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coalgebraic Approach to the Loday Infinity Category, Stem Differential
  for $2n$-ary Graded and Homotopy Algebras   We define a graded twisted-coassociative coproduct on the tensor algebra $TW$
of any $\Z^n$-graded vector space $W$. If $W$ is the desuspension space $\da V$
of a graded vector space $V$, the coderivations (resp. quadratic ``degree 1''
codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1
with sequences $\zp_s$, $s\ge 1$, of $s$-linear maps on $V$ (resp.
$\Z^n$-graded Loday structures on $V$, sequences that we call Loday infinity
structures on $V$). We prove a minimal model theorem for Loday infinity
algebras, investigate Loday infinity morphisms, and observe that the
$\op{Lod}_{\infty}$ category contains the $\op{L}_{\infty}$ category as a
subcategory. Moreover, the graded Lie bracket of coderivations gives rise to a
graded Lie ``stem'' bracket on the cochain spaces of graded Loday, Loday
infinity, and $2n$-ary graded Loday algebras (the latter extend the
corresponding Lie algebras in the sense of Michor and Vinogradov). These
algebraic structures have square zero with respect to the stem bracket, so that
we obtain natural cohomological theories that have good properties with respect
to formal deformations. The stem bracket restricts to the graded
Nijenhuis-Richardson and--up to isomorphism--to the Grabowski-Marmo brackets
(the last bracket extends the Schouten-Nijenhuis bracket to the space of graded
antisymmetric first order polydifferential operators), and it encodes, beyond
the already mentioned cohomologies, those of graded Lie, graded Poisson, graded
Jacobi, Lie infinity, as well as that of $2n$-ary graded Lie algebras.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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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: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph