Esta memoria está dedicada al estudio de la teoría de homotopía de álgebras operádicas y sus aplicaciones en teoría cuántica ...

Without doubts, calculating homotopy groups of spheres is one of the main open problems in Algebraic Topology. After Toda ...

En este trabajo definimos una teoría de cohomología para conjuntos simpliciales entendidos como ∞-categorías. Tras su ...

Una representación de un quiver es una colección de espacios vectoriales y aplicaciones lineales indexadas por un grafo ...

We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure ...

We describe the role of the Schur multiplier in the structure of the p-torsion of discrete groups. More concretely, we ...

We define a K-theory for pointed right derivators and show that it agrees with Waldhausen K-theory in the case where the ...

Derived A-algebras are derived and homotopy invariant versions of differential graded algebras. They were introduced by ...

We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic ...

We consider the following problems in a well generated triangulated category T . Let α be a regular cardinal and T α ⊂ T ...

We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for ...

In this paper we show how to modify cofibrations in a monoidal model category so that the tensor unit becomes cofibrant ...

We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal ...

We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We ...

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A∞-algebras of Fukaya-Oh-Ohta-Ono.

We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a ...

In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric monoidal model categories. We first ...

In this paper we show an example of two differential graded algebras that have the same derivator K-theory but non-isomorphic ...

The primary algebraic model of a ring spectrum R is the ring π∗R of homotopy groups. We introduce the secondary model π∗,∗R ...

We endow categories of nonsymmetric operads with natural model structures. We work with no restriction on our operads and ...

Isabel Fernández, de la Universidad de Sevilla, es conferenciante invitada junto con Pablo Mira (Universidad Politécnica ...

In this paper we prove the laws of Toda brackets on the homotopy groups of a connective ring spectrum and the laws of the cup-one square in the homotopy groups of a commutative connective ring spectrum.

We show that the symmetric track groups Sym(n), which are extensions of the symmetric groups Sym(n) associated to the second Stiefel-Whitney class, act as crossed modules on the secondary homotopy groups of a pointed space.

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered.

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track ...

We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally ...

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full ...

In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain ...

The concept of a triangulated homotopy category can be canonically lifted to the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated category.

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity ...