Related papers: The Operadic Nerve, Relative Nerve, and the Grothe…

In this paper, we utilize the framework of Markov processes to attain a more probabilistic perspective on the theory of transfer operators. In doing so, we establish a functional central limit theorem (FLCT) for an $O(N)$ model associated…

We study correlation functions with multiple averaged null energy (ANEC) operators in conformal field theories. For large $N$ CFTs with a large gap to higher spin operators, we show that the OPE between a local operator and the ANEC can be…

In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some `one particle space' $\K$ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of…

Let M be a bicomplete, closed symmetric monoidal category. Let P be an operad in M, i.e., a monoid in the category of symmetric sequences of objects in M, with its composition monoidal structure. Let R be a P-co-ring, i.e., a comonoid in…

We discuss right fibrations in the $\infty$-categorical context of Segal objects in a category V and prove some basic results about these.

Let $\mathcal{C}$ be a finite tensor category, and let $\mathcal{M}$ be an exact left $\mathcal{C}$-module category. The relative Serre functor of $\mathcal{M}$ is an endofunctor $\mathbb{S}$ on $\mathcal{M}$ together with a natural…

The Grothendieck construction is a classical correspondence between diagrams of categories and coCartesian fibrations over the indexing category. In this paper we consider the analogous correspondence in the setting of model categories. As…

In this article we study a relative monoidal version of the Bondal-Orlov reconstruction theorem. We establish an uniqueness result for tensor triangulated category structures $(\boxtimes,\mathbb{1})$ on the derived category $D^{b}(X)$ of a…

The study of Frobenius algebras in the category $\mathbf{Rel}$ via their nerve functor into simplicial sets has been introduced recently. In this article, we focus on the particular case of effect algebras and pseudo effect algebras and…

We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before…

Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right derived functors of section functors with supports in…

We construct for every $\infty$-operad $\mathcal{O}^\otimes$ with certain finite limits new $\infty$-operads of spectrum objects and of commutative group objects in $\mathcal{O}$. We show that these are the universal stable resp. additive…

If $f:S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes: \mathcal H_*(S') \to\mathcal H_*(S)$, where $\mathcal H_*(S)$ is the pointed unstable motivic homotopy category over…

We clarify the relationship between Grothendieck duality \`a la Neeman and the Wirthm\"uller isomorphism \`a la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated…

For an endofunctor $F\colon\mathcal{C}\to\mathcal{C}$ on an ($\infty$-)category $\mathcal{C}$ we define the $\infty$-category $\operatorname{Cart}(\mathcal{C},F)$ of generalized Cartier modules as the lax equalizer of $F$ and the identity.…

We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical nerves. It is shown that every necklicial nerve can be…

We prove that for a topological operad $P$ the operad of oriented cubical chains, $C^{ord}_\ast(P)$, and the operad of singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{ord}_\ast(P;\mathbb{Q})$ is formal if and only…

In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtained by the author in the book "Homotopy of operads and…