Related papers: Weak sectional category
We investigate if an existing notion of weak sequential convergence in a Hadamard space can be induced by a topology. We provide an answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown…
In [BaSc2], the author and Tomer Schlank introduced a much weaker homotopical structure than a model category, which we called a "weak cofibration category". We further showed that a small weak cofibration category induces in a natural way…
We define weak units in a semi-monoidal 2-category $\CC$ as cancellable pseudo-idempotents: they are pairs $(I,\alpha)$ where $I$ is an object such that tensoring with $I$ from either side constitutes a biequivalence of $\CC$, and $\alpha:…
We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, "weak" implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along…
We propose a notion of weak (n+k,n)-category, which we call (n+k,n)-Theta-spaces. The (n+k,n)-Theta-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal's…
We introduce a dependent type theory whose models are weak {\omega}-categories, generalizing Brunerie's definition of {\omega}-groupoids. Our type theory is based on the definition of {\omega}-categories given by Maltsiniotis, himself…
We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of…
We consider four categories: the category of diagrams of small categories indexed by a given small category O, the (comma) category of small categories over O, the category of diagrams of simplicial sets indexed by O, and the category of…
Weak bimonoids in duoidal categories are introduced. They provide a common generalization of bimonoids in duoidal categories and of weak bimonoids in braided monoidal categories. Under the assumption that idempotent morphisms in the base…
We introduce the notion of groupoidal (weak) test category, which is a small category A such that the groupoid-valued presheaves over A models homotopy types in a "canonical and nice" way. The definition does not require a priori that A is…
We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and…
Gambino and Garner proved that the syntactic category of a dependent type theory with identity types can be endowed with a weak factorization system structure, called identity type weak factorization system. In this paper we consider an…
We define and study an equivariant version of Farber's topological complexity for spaces with a given compact group action. This is a special case of the equivariant sectional category of an equivariant map, also defined in this paper. The…
In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. If $H$ is a weak monoidal Hom-Hopf algebra with bijective antipode and let $Aut_{wmHH}(H)$ be the…
Many definitions of weak n-category have been proposed. It has been widely observed that each of these definitions is of one of two types: algebraic definitions, in which composites and coherence cells are explicitly specified, and…
A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…
We study monoidal structures on the category of (co)modules over a weak bialgebra. Results due to Nill and Szlach\'anyi are unified and extended to infinite algebras. We discuss the coalgebra structure on the source and target space of a…
Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphism on homology. In the other, the weak equivalences are maps…
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…
A multicategory is what remains of a monoidal category when monoidal product is not available. A weak multicategory means that hom-sets are in fact categories, and in place of usual equations, there are natural isomorphisms, which have to…