Related papers: Left determined model structures for locally prese…

We give a general method to build categories of combinatorial manifolds, i.e. categories of combinatorial objects satisfying some local property at every "point", as coreflective subcategories of categories of relational presheaves. To do…

Generalizing Eisenbud's matrix factorizations, we define factorization categories. Following work of Positselski, we define their associated derived categories. We construct specific resolutions of factorizations built from a choice of…

We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous…

Fong developed `decorated cospans' to model various kinds of open systems: that is, systems with inputs and outputs. In this framework, open systems are seen as the morphisms of a category and can be composed as such, allowing larger open…

We extend the previously established zesting techniques from fusion categories to general tensor categories. In particular we consider the category of comodules over a Hopf algebra, providing a detailed translation of the categorical…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentable additive category. In particular, this is true in any…

It is well-known that Polish Roelcke precompact groups are the groups that can be represented as automorphism groups of $\aleph_0$-categorical structures in continuous logic and that there is a precise correspondence between properties of…

We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to…

In this paper we describe two ways on which cofibred categories give rise to bisimplicial sets. The "fibred nerve" is a natural extension of Segal's classical nerve of a category, and it constitutes an alternative simplicial description of…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

In [BaSc2] the authors introduced a much weaker homotopical structure than a model category, called a "weak cofibration category". We further showed that a small weak cofibration category induces in a natural way a model category structure…

We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical…

This work can be thought as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a two-sorted structure). We show that if one of the two…

We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…

We define a commutative monoid structure on the poset of left-exact localizations of a higher topos, that we call the acyclic product. Our approach is anchored in a structural analogy between the poset of left-exact localizations of a topos…

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…

We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms between Grothendieck topoi. We discuss properties of both…

Let $\mathcal C$ be the category of finite graphs. Lov\`{a}sz shows that the semi-ring of isomorphism classes of $\mathcal C$ (with coproduct as sum, and product as multiplication) is embedded into the direct product of the semi-ring of…