Now showing items 1-20 of 30

    • Icon

      2º Congreso de Jóvenes Investigadores  [Article]

      Gancedo García, Francisco; Muro Jiménez, Fernando (Real Sociedad Matematica Española, 2013)
    • Icon

      A note on K-theory and triangulated derivators  [Article]

      Muro Jiménez, Fernando; Raptis, George (Elsevier, 2011-08-01)
      In this paper we show an example of two differential graded algebras that have the same derivator K-theory but non-isomorphic Waldhausen K-theory. We also prove that Maltsiniotis’s comparison and localization conjectures ...
    • Icon

      Cylinders for non-symmetric DG-operads via homological perturbation theory  [Article]

      Muro Jiménez, Fernando (Elsevier, 2016-09)
      We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity ...
    • Icon

      Derived homotopy algebras  [PhD Thesis]

      Maes, Jeroen (2016-10-28)
      Derived A-algebras are derived and homotopy invariant versions of differential graded algebras. They were introduced by Steffen Sagave in 20 0 in order to construct minimal models for diferential graded algebras over ...
    • Icon

      Dwyer-Kan homotopy theory of enriched categories  [Article]

      Muro Jiménez, Fernando (London Mathematical Society, 2015)
      We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer–Kan equivalences, i.e. ...
    • Icon

      Entrevista a Isabel Fernández, conferenciante invitada al ICM 2010  [Article]

      Muro Jiménez, Fernando (Real Sociedad Matematica Española, 2010)
      Isabel Fernández, de la Universidad de Sevilla, es conferenciante invitada junto con Pablo Mira (Universidad Politécnica de Cartagena) a la sección de Geometría del próximo ICM, que se celebrará en agosto en Hyderabad ...
    • Icon

      Homotopy theory of bicomplexes  [Article]

      Muro Jiménez, Fernando; Roitzheim, Constanze (Elsevier, 2019-05)
      We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure’s weak ...
    • Icon

      Homotopy theory of non-symmetric operads, II: Change of base category and left properness  [Article]

      Muro Jiménez, Fernando (Mathematical Sciences Publishers, 2014)
      We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model ...
    • Icon

      Homotopy theory of nonsymmetric operads  [Article]

      Muro Jiménez, Fernando (Mathematical Sciences Publishers, 2011)
      We endow categories of nonsymmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also ...
    • Icon

      Homotopy units in A-infinity algebras  [Article]

      Muro Jiménez, Fernando (American Mathematical Society, 2016-03)
      We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative ...
    • Icon

      K-theory of derivators revisited  [Article]

      Muro Jiménez, Fernando; Raptis, George (Mathematical Sciences Publishers, 2017)
      We define a K-theory for pointed right derivators and show that it agrees with Waldhausen K-theory in the case where the derivator arises from a good Waldhausen category. This K-theory is not invariant under general ...
    • Icon

      Maltsiniotis's first conjecture for K1  [Article]

      Muro Jiménez, Fernando (Duke University Press, 2008)
      We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences ...
    • Icon

      Moduli spaces of algebras over non-symmetric operads  [Article]

      Muro Jiménez, Fernando (2014)
      In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric monoidal model categories. We first compute the homotopy fiber of the forgetful functor sending an algebra to its underlying object, ...
    • Icon

      On determinant functors and K-theory  [Article]

      Muro Jiménez, Fernando; Tonks, Andrew; Witte, Malte (Universitat Autònoma de Barcelona, 2015)
      We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for ...
    • Icon

      On the functoriality of cohomology of categories  [Article]

      Muro Jiménez, Fernando (Elsevier, 2006-03)
      In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain ...
    • Icon

      On the unit of a monoidal model category  [Article]

      Muro Jiménez, Fernando (Elsevier, 2015-08-15)
      In this paper we show how to modify cofibrations in a monoidal model category so that the tensor unit becomes cofibrant while keeping the same weak equivalences. We obtain aplications to enriched categories and coloured ...
    • Icon

      Representaciones de Quivers  [Final Degree Work]

      Linares Torres, Javier (2019-06)
      Una representación de un quiver es una colección de espacios vectoriales y aplicaciones lineales indexadas por un grafo dirigido: el quiver. En este trabajo damos una introducción a la teoría de representaciones de quivers ...
    • Icon

      Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology  [Article]

      Muro Jiménez, Fernando (Springer, 2004)
      In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the ...
    • Icon

      Secondary homotopy groups  [Article]

      Baues, Hans Joachim; Muro Jiménez, Fernando (De Gruyter, 2008-07)
      Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also ...
    • Icon

      Smash products for secondary homotopy groups  [Article]

      Bauer, Hans Joachim; Muro Jiménez, Fernando (Springer, 2008-10)
      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.