Results 41 to 50 of about 120 (113)

Operadic and Diagrammatic Semantics of the Greimas Semiotic Square

Axioms
We develop a categorical and operadic semantics for the diagrammatic proof system underlying the Greimas semiotic square. Building on a prior proof-theoretic formulation, we extract a typed signature of diagrammatic inference rules and construct the ...
Michael Fowler
doaj   +1 more source

Hinich's model for Day convolution revisited

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We prove that Hinich's construction of the Day convolution operad of two O$\mathcal {O}$‐monoidal ∞$\infty$‐categories is an exponential in the ∞$\infty$‐category of ∞$\infty$‐operads over O$\mathcal {O}$, and use this to give an explicit description of the formation of algebras in the Day convolution operad as a bivariant functor.
Christoph Winges
wiley   +1 more source

Jordan Triples and Operads

Journal of Algebra, 2000
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Gnedbaye, Allahtan Victor, Wambst, Marc
openaire   +2 more sources

Hom ω$\omega$‐categories of a computad are free

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We provide a new description of the hom functor on weak ω$\omega$‐categories, and show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict ω$\omega$‐categories.
Thibaut Benjamin, Ioannis Markakis
wiley   +1 more source

From homotopy operads to infinity-operads [PDF]

Journal of Noncommutative Geometry, 2017
The goal of the present paper is to compare, in a precise way, two approaches of operads up to homotopy which appear in the literature. Namely, we construct a functor from the category of strict unital homotopy colored operads to the category of infinity-operads. The former notion, that we make precise, is the operadic generalization of the notion of A-
openaire   +3 more sources

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source

Parametrized stability and the universal property of global spectra

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop a framework of parametrized semiadditivity and stability with respect to so‐called atomic orbital subcategories of an indexing ∞$\infty$‐category T$T$, extending work of Nardin. Specializing this framework, we introduce global ∞$\infty$‐categories and the notions of equivariant semiadditivity and stability, yielding a higher ...
Bastiaan Cnossen, Tobias Lenz, Sil Linskens   +2 more
wiley   +1 more source

The Operadic Theory of Convexity

Applied Categorical Structures
In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\scr{O}$-monoidal categories, we state and prove a Grothendieck construction for lax $\scr{O}$-monoidal functors into convex sets. We
HADERI, REDI, Stern, Walker H., Okay, Cihan   +2 more
openaire   +4 more sources

The symmetric join operad [PDF]

Homology, Homotopy and Applications, 2013
The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad which includes the symmetries given by permutations of the factors of the join. From this combinatorics we construct an E-infinity operad which coacts naturally on the chains of a simplicial set.
Adamaszek, Michał, Jones, John D. S.
openaire   +3 more sources

Structure theorems for braided Hopf algebras

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley   +1 more source