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Browsing Álgebra by Author "Muro Jiménez, Fernando"
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A note on Ktheory and triangulated derivators [Article]
Muro Jiménez, Fernando; Raptis, George (Elsevier, 20110801)In this paper we show an example of two differential graded algebras that have the same derivator Ktheory but nonisomorphic Waldhausen Ktheory. We also prove that Maltsiniotis’s comparison and localization conjectures ...

Cylinders for nonsymmetric DGoperads via homological perturbation theory [Article]
Muro Jiménez, Fernando (Elsevier, 201609)We construct small cylinders for cellular nonsymmetric DGoperads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the Ainfinity ...

DwyerKan 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. ...

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 ...

Homotopy theory of bicomplexes [Article]
Muro Jiménez, Fernando; Roitzheim, Constanze (Elsevier, 201905)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 ...

Homotopy theory of nonsymmetric 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 (nonsymmetric) operads, and also between model ...

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 ...

Homotopy units in Ainfinity algebras [Article]
Muro Jiménez, Fernando (American Mathematical Society, 201603)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 ...

Ktheory of derivators revisited [Article]
Muro Jiménez, Fernando; Raptis, George (Mathematical Sciences Publishers, 2017)We define a Ktheory for pointed right derivators and show that it agrees with Waldhausen Ktheory in the case where the derivator arises from a good Waldhausen category. This Ktheory is not invariant under general ...

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 ...

Moduli spaces of algebras over nonsymmetric 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, ...

On determinant functors and Ktheory [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 ...

On the functoriality of cohomology of categories [Article]
Muro Jiménez, Fernando (Elsevier, 200603)In this paper we show that the BauesWirsching complex used to define cohomology of categories is a 2functor from a certain 2category of natural systems of abelian groups to the 2category of chain complexes, chain ...

On the unit of a monoidal model category [Article]
Muro Jiménez, Fernando (Elsevier, 20150815)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 ...

Representation theory of some infinitedimensional 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 ...

Secondary homotopy groups [Article]
Baues, Hans Joachim; Muro Jiménez, Fernando (De Gruyter, 200807)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 ...

Smash products for secondary homotopy groups [Article]
Bauer, Hans Joachim; Muro Jiménez, Fernando (Springer, 200810)We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cupone products, Toda brackets and Whitehead products are considered.

Teoría de representaciones, invariantes cohomológicos y tipos de homotopía propia [PhD Thesis]
Muro Jiménez, Fernando (2004) 
The 1type of a Waldhausen Ktheory spectrum [Article]
Muro Jiménez, Fernando; Tonks, Andrew (Elsevier, 20071201)We give a small functorial algebraic model for the 2stage Postnikov section of the Ktheory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.

The algebra of secondary homotopy operations in ring spectra [Article]
Baues, Hans Joachim; Muro Jiménez, Fernando (London Mathematical Society, 2011)The primary algebraic model of a ring spectrum R is the ring π∗R of homotopy groups. We introduce the secondary model π∗,∗R which has the structure of a secondary analogue of a ring. The homology of π∗,∗R is π∗R and ...