相关论文: Generalized operads and their inner cohomomorphism…

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case,…

Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the last decades. They can be thought of as symmetric monoidal…

We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…

On construit des foncteurs de formes differentielles generalisees. Ceux-ci, dans le cas d'espaces nilpotents de type fini, determinent le type d'homotopie faible des espaces. Ils sont munis, d'une maniere elementaire et naturelle, de…

We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

We provide a generalized treatment of (co)cartesian arrows, fibrations, and functors. Compared to the classical conditions, the endpoint inclusions get replaced by arbitrary shape inclusions. Our framework is Riehl--Shulman's simplicial…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

Operads were originally defined by May to have right actions of the symmetric groups, but later formulations have also used no groups actions at all or group actions by such families as the braid groups. We call such families action…

This article generalizes the operad of moduli spaces of curves to SUSY curves. SUSY curves are algebraic curves with additional supersymmetric or supergeometric structure. Here, we focus on the description of the relevant category of graphs…

The notion of 2--monoidal category used here was introduced by B.~Vallette in 2007 for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the category of quadratic algebras (that is,…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.

We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show…

The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

For $\mathcal{O}$ a reduced operad, a generalized divergence from the derivations of a free $\mathcal{O}$-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the…

This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…

The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As…