Author profile: Muro Jiménez, Fernando
Institutional data
Name | Muro Jiménez, Fernando |
Department | Algebra |
Knowledge area | Álgebra |
Professional category | Catedrático de Universidad |
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Statistics
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No. publications
33
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No. visits
5456
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7467
Publications |
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PhD Thesis
On homotopical algebra and quantum field theories
(2023)
Esta memoria está dedicada al estudio de la teoría de homotopía de álgebras operádicas y sus aplicaciones en teoría cuántica ... |
Master's Final Project
La sucesión espectral de Adams
(2022)
Without doubts, calculating homotopy groups of spheres is one of the main open problems in Algebraic Topology. After Toda ... |
Master's Final Project
Cohomology of infinity-categories
(2022)
En este trabajo definimos una teoría de cohomología para conjuntos simpliciales entendidos como ∞-categorías. Tras su ... |
Final Degree Project
Representaciones de Quivers
(2019)
Una representación de un quiver es una colección de espacios vectoriales y aplicaciones lineales indexadas por un grafo ... |
Article
Homotopy theory of bicomplexes
(Elsevier, 2019)
We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure ... |
Article
Torsion homology and cellular approximation
(Mathematical Sciences Publishers, 2019)
We describe the role of the Schur multiplier in the structure of the p-torsion of discrete groups. More concretely, we ... |
Article
K-theory of derivators revisited
(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 ... |
PhD Thesis
Derived homotopy algebras
(2016)
Derived A-algebras are derived and homotopy invariant versions of differential graded algebras. They were introduced by ... |
Article
Cylinders for non-symmetric DG-operads via homological perturbation theory
(Elsevier, 2016)
We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic ... |
Article
Transfinite Adams representability
(Elsevier, 2016)
We consider the following problems in a well generated triangulated category T . Let α be a regular cardinal and T α ⊂ T ... |
Article
Homotopy units in A-infinity algebras
(American Mathematical Society, 2016)
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for ... |
Article
On the unit of a monoidal model category
(Elsevier, 2015)
In this paper we show how to modify cofibrations in a monoidal model category so that the tensor unit becomes cofibrant ... |
Article
Dwyer-Kan homotopy theory of enriched categories
(London Mathematical Society, 2015)
We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal ... |
Article
On determinant functors and K-theory
(Universitat Autònoma de Barcelona, 2015)
We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We ... |
Article
Unital associahedra
(De Gruyter, 2014)
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. |
Article
Homotopy theory of non-symmetric operads, II: Change of base category and left properness
(Mathematical Sciences Publishers, 2014)
We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a ... |
Article
Moduli spaces of algebras over non-symmetric operads
(2014)
In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric monoidal model categories. We first ... |
Article
2º Congreso de Jóvenes Investigadores
(Real Sociedad Matematica Española, 2013)
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Article
A note on K-theory and triangulated derivators
(Elsevier, 2011)
In this paper we show an example of two differential graded algebras that have the same derivator K-theory but non-isomorphic ... |
Article
The algebra of secondary homotopy operations in ring spectra
(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 ... |
Article
Homotopy theory of nonsymmetric operads
(Mathematical Sciences Publishers, 2011)
We endow categories of nonsymmetric operads with natural model structures. We work with no restriction on our operads and ... |
Article
Entrevista a Isabel Fernández, conferenciante invitada al ICM 2010
(Real Sociedad Matematica Española, 2010)
Isabel Fernández, de la Universidad de Sevilla, es conferenciante invitada junto con Pablo Mira (Universidad Politécnica ... |
Article
Toda brackets and cup-one squares for ring spectra
(Taylor & Francis, 2009)
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. |
Article
The symmetric action on secondary homotopy groups
(The Belgian Mathematical Society, 2008)
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. |
Article
Smash products for secondary homotopy groups
(Springer, 2008)
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. |
Article
Secondary homotopy groups
(De Gruyter, 2008)
Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track ... |
Article
Maltsiniotis's first conjecture for K1
(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 ... |
Article
The 1-type of a Waldhausen K-theory spectrum
(Elsevier, 2007)
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. |
Article
Triangulated categories without models
(Springer, 2007)
We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full ... |
Article
On the functoriality of cohomology of categories
(Elsevier, 2006)
In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain ... |
Article
The characteristic cohomology class of a triangulated category
(2005)
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. |
Article
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
(Springer, 2004)
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity ... |
PhD Thesis |