Results 51 to 60 of about 92 (88)
Operads, Homotopy Theory and Higher Categories in Algebraic Quantum Field Theory
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
Benini M., Schenkel A.
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Higher operad structure for Fukaya categories
Operads often arise from geometry. The standard $A_\infty$ operad can be derived from the cellular chains on the Stasheff associahedra, and an $A_\infty$ algebra is an algebra over this operad. The notion of an $\mathbf{fc}$-multicategory, also called a virtual double category, is a two-dimensional generalization of operads and multicategories.
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Weak units, higher operads, and deformations of monoidal categories
, 2022 Abstract: Differentially graded categories (abbreviated: dg-categories) are fundamental objects in algebraic geometry and higher category theory. After their introduction by Kelly to homologous algebra, dg-categories were used by Bondal-Kapranov to enhance triangulated categories.
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On higher structure on the operadic deformation complexes ${Def}(e_n\to \mathcal{P})$
, 2017 In this paper, we prove that there is a canonical homotopy $(n+1)$-algebra structure on the shifted operadic deformation complex $Def(e_n\to\mathcal{P})[-n]$ for any operad $\mathcal{P}$ and a map of operads $f\colon e_n\to\mathcal{P}$. This result generalizes the result of [T2], where the case $\mathcal{P}=\mathrm{End}_{Op}(X)$ was considered. Another
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Matriarch: A Python Library for Materials Architecture. [PDF]
ACS Biomater Sci Eng, 2015 Giesa T +3 more
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Higher crossed modules of algebras over an operad
We study crossed modules in the context of algebras over an operad. To do so, in the first section, we adapt the methods of Janelidze by reviewing the notions of internal actions, precrossed modules and crossed modules in the operadic case. Moreover, we extract the Peiffer relations, well known in the Lie case, for precrossed modules over an arbitrary ...
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$\omega$-Operads of Coendomorphisms for Higher Structures
, 2012 Comment: 53 ...
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Cyclic operads, dendroidal structures, higher categories
, 2010 The thesis consists of three parts, each of these parts contributes to the theory of operads with some new results. In the first part we study the homotopy theory of cyclic operads by employing methods developed by Berger and Moerdijk for the study of the homotopy theory of operads.
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A higher Mackey functor description of algebras over an $N_{\infty}$-operad
Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding $\infty$-category of higher incomplete $\mathcal{I}$-Mackey functors with value in spaces.
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