Welcome to my website! I'm a professor of mathematics at the University of Seville. Here, you'll mostly find information about my research.
Find Out MoreI work on algebraic topology, specifically on homotopy theory, and I also interact with related fields such as category theory, homological algebra, K-theory, and representation theory.
Encontrarás toda la información referente a la asignatura en el campus virtual: horario de tutorías, documentos de interés, calificaciones, avisos... Ese será nuestro cauce de comunicación durante el curso. También puedes escribirme un correo electrónico cuando lo necesites.
Campus virtualI got my PhD at the Universidad de Sevilla in 2004. Then I spent two years at the Max-PlanckInstitut für Mathematik and two and a half years at the Universitat de Barcelona as a postdoc. I moved back to Seville in 2009 with an associate professorship and became a full professor in 2023. Here, I'm a member of the Mathematical Institute and of the Algebra Department.
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@inbook{Jasso_2024,
title={The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence},
ISBN={9783031577895},
ISSN={2197-8549},
url={http://dx.doi.org/10.1007/978-3-031-57789-5_4},
DOI={10.1007/978-3-031-57789-5_4},
booktitle={Triangulated Categories in Representation Theory and Beyond},
publisher={Springer Nature Switzerland},
author={Jasso, Gustavo and Keller, Bernhard and Muro, Fernando},
year={2024},
pages={105–140} }
@article{Jasso_2026,
title={The derived Auslander-Iyama correspondence},
ISSN={0894-0347},
url={http://dx.doi.org/10.1090/jams/1079},
DOI={10.1090/jams/1079},
journal={Journal of the American Mathematical Society},
publisher={American Mathematical Society (AMS)},
author={Jasso, Gustavo and Muro, Fernando and Keller, Bernhard},
year={2026},
month=May }
@article{Muro_2007,
title={Triangulated categories without models},
volume={170},
ISSN={1432-1297},
url={http://dx.doi.org/10.1007/s00222-007-0061-2},
DOI={10.1007/s00222-007-0061-2},
number={2},
journal={Inventiones mathematicae},
publisher={Springer Science and Business Media LLC},
author={Muro, Fernando and Schwede, Stefan and Strickland, Neil},
year={2007},
month=May,
pages={231–241} }
@article{Muro_2011,
title={Homotopy theory of nonsymmetric operads},
volume={11},
ISSN={1472-2747},
url={http://dx.doi.org/10.2140/agt.2011.11.1541},
DOI={10.2140/agt.2011.11.1541},
number={3},
journal={Algebraic & Geometric Topology},
publisher={Mathematical Sciences Publishers},
author={Muro, Fernando},
year={2011},
month=May,
pages={1541–1599} }
@article{Baues_2007,
title={The homotopy category of pseudofunctors and translation cohomology},
volume={211},
ISSN={0022-4049},
url={http://dx.doi.org/10.1016/j.jpaa.2007.04.008},
DOI={10.1016/j.jpaa.2007.04.008},
number={3},
journal={Journal of Pure and Applied Algebra},
publisher={Elsevier BV},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2007},
month=Dec,
pages={821–850} }
@article{Baues_2008,
title={Secondary homotopy groups},
volume={20},
ISSN={1435-5337},
url={http://dx.doi.org/10.1515/FORUM.2008.032},
DOI={10.1515/forum.2008.032},
number={4},
journal={Forum Mathematicum},
publisher={Walter de Gruyter GmbH},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2008},
month=Jan }
@article{Baues_2008,
title={Cohomologically triangulated categories I},
volume={1},
ISSN={1865-5394},
url={http://dx.doi.org/10.1017/is007011018jkt019},
DOI={10.1017/is007011018jkt019},
number={1},
journal={Journal of K-Theory},
publisher={Cambridge University Press (CUP)},
author={Baues, H.-J. and Muro, F.},
year={2008},
month=Jan,
pages={3–48} }
@article{Baues_2007,
title={Smash Products for Secondary Homotopy Groups},
volume={16},
ISSN={1572-9095},
url={http://dx.doi.org/10.1007/s10485-007-9071-x},
DOI={10.1007/s10485-007-9071-x},
number={5},
journal={Applied Categorical Structures},
publisher={Springer Science and Business Media LLC},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2007},
month=Oct,
pages={551–616} }
@article{Baues_2010,
title={The algebra of secondary homotopy operations in ring spectra},
volume={102},
ISSN={0024-6115},
url={http://dx.doi.org/10.1112/plms/pdq034},
DOI={10.1112/plms/pdq034},
number={4},
journal={Proceedings of the London Mathematical Society},
publisher={Wiley},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2010},
month=Nov,
pages={637–696} }
@article{Baues_2008,
title={Cohomologically triangulated categories II},
volume={3},
ISSN={1865-5394},
url={http://dx.doi.org/10.1017/is008007021jkt061},
DOI={10.1017/is008007021jkt061},
number={1},
journal={Journal of K-Theory},
publisher={Cambridge University Press (CUP)},
author={Baues, H.-J. and Muro, F.},
year={2008},
month=Dec,
pages={1–52} }
@article{Muro_2012,
title={Unital associahedra},
volume={26},
ISSN={1435-5337},
url={http://dx.doi.org/10.1515/forum-2011-0130},
DOI={10.1515/forum-2011-0130},
number={2},
journal={Forum Mathematicum},
publisher={Walter de Gruyter GmbH},
author={Muro, Fernando and Tonks, Andrew},
year={2012},
month=Feb,
pages={593–620} }
@article{Baues_2008,
title={The symmetric action on secondary homotopy groups},
volume={15},
ISSN={1370-1444},
url={http://dx.doi.org/10.36045/bbms/1225893951},
DOI={10.36045/bbms/1225893951},
number={4},
journal={Bulletin of the Belgian Mathematical Society - Simon Stevin},
publisher={The Belgian Mathematical Society},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2008},
month=May }
@article{Baues_2009,
title={Toda Brackets and Cup-One Squares for Ring Spectra},
volume={37},
ISSN={1532-4125},
url={http://dx.doi.org/10.1080/00927870802241188},
DOI={10.1080/00927870802241188},
number={1},
journal={Communications in Algebra},
publisher={Informa UK Limited},
author={Baues, Hans-Joachim and Muro, Fernando},
year={2009},
month=Jan,
pages={56–82} }
@misc{baues2005characteristiccohomologyclasstriangulated,
title={The characteristic cohomology class of a triangulated category},
author={H. -J. Baues and F. Muro},
year={2005},
eprint={math/0505540},
archivePrefix={arXiv},
primaryClass={math.KT},
url={https://arxiv.org/abs/math/0505540},
}
@article{Muro_2007,
title={The 1-type of a Waldhausen K-theory spectrum},
volume={216},
ISSN={0001-8708},
url={http://dx.doi.org/10.1016/j.aim.2007.05.008},
DOI={10.1016/j.aim.2007.05.008},
number={1},
journal={Advances in Mathematics},
publisher={Elsevier BV},
author={Muro, Fernando and Tonks, Andrew},
year={2007},
month=Dec,
pages={178–211} }
@article{Muro_2014,
title={Homotopy theory of non-symmetric operads, II: Change of base category and left properness},
volume={14},
ISSN={1472-2747},
url={http://dx.doi.org/10.2140/agt.2014.14.229},
DOI={10.2140/agt.2014.14.229},
number={1},
journal={Algebraic & Geometric Topology},
publisher={Mathematical Sciences Publishers},
author={Muro, Fernando},
year={2014},
month=Jan,
pages={229–281} }
@article{Muro_2006,
title={On the functoriality of cohomology of categories},
volume={204},
ISSN={0022-4049},
url={http://dx.doi.org/10.1016/j.jpaa.2005.05.004},
DOI={10.1016/j.jpaa.2005.05.004},
number={3},
journal={Journal of Pure and Applied Algebra},
publisher={Elsevier BV},
author={Muro, Fernando},
year={2006},
month=Mar,
pages={455–472} }
@article{Muro_2015,
title={On the unit of a monoidal model category},
volume={191},
ISSN={0166-8641},
url={http://dx.doi.org/10.1016/j.topol.2015.05.006},
DOI={10.1016/j.topol.2015.05.006},
journal={Topology and its Applications},
publisher={Elsevier BV},
author={Muro, Fernando},
year={2015},
month=Aug,
pages={37–47} }
@article{Muro_2004,
title={Suspensions of crossed and quadratic complexes, co-H-structures and applications},
volume={357},
ISSN={0002-9947},
url={http://dx.doi.org/10.1090/S0002-9947-04-03597-4},
DOI={10.1090/s0002-9947-04-03597-4},
number={9},
journal={Transactions of the American Mathematical Society},
publisher={American Mathematical Society (AMS)},
author={Muro, Fernando},
year={2004},
month=Dec,
pages={3623–3653} }
@inbook{Muro_2008,
title={On K_1 of a Waldhausen category},
ISBN={9783037195604},
ISSN={2523-5168},
url={http://dx.doi.org/10.4171/060-1/4},
DOI={10.4171/060-1/4},
booktitle={K-Theory and Noncommutative Geometry},
publisher={EMS Press},
author={Muro, Fernando and Tonks, Andrew},
year={2008},
month=Oct,
pages={91–115} }
@article{Muro_2019,
title={Homotopy theory of bicomplexes},
volume={223},
ISSN={0022-4049},
url={http://dx.doi.org/10.1016/j.jpaa.2018.08.007},
DOI={10.1016/j.jpaa.2018.08.007},
number={5},
journal={Journal of Pure and Applied Algebra},
publisher={Elsevier BV},
author={Muro, Fernando and Roitzheim, Constanze},
year={2019},
month=May,
pages={1913–1939} }
@article{Muro_2015,
title={Homotopy units in 𝐴-infinity algebras},
volume={368},
ISSN={0002-9947},
url={http://dx.doi.org/10.1090/tran/6545},
DOI={10.1090/tran/6545},
number={3},
journal={Transactions of the American Mathematical Society},
publisher={American Mathematical Society (AMS)},
author={Muro, Fernando},
year={2015},
month=May,
pages={2145–2184} }
@article{Muro_2015,
title={Dwyer-Kan homotopy theory of enriched categories},
volume={8},
ISSN={1753-8416},
url={http://dx.doi.org/10.1112/jtopol/jtu029},
DOI={10.1112/jtopol/jtu029},
number={2},
journal={Journal of Topology},
publisher={Wiley},
author={Muro, Fernando},
year={2015},
month=Mar,
pages={377–413} }
@article{Muro_2020,
title={ENHANCED FINITE TRIANGULATED CATEGORIES},
volume={21},
ISSN={1475-3030},
url={http://dx.doi.org/10.1017/S1474748020000250},
DOI={10.1017/s1474748020000250},
number={3},
journal={Journal of the Institute of Mathematics of Jussieu},
publisher={Cambridge University Press (CUP)},
author={Muro, Fernando},
year={2020},
month=June,
pages={741–783} }
@article{Muro_2014,
title={Moduli spaces of algebras over nonsymmetric operads},
volume={14},
ISSN={1472-2747},
url={http://dx.doi.org/10.2140/agt.2014.14.1489},
DOI={10.2140/agt.2014.14.1489},
number={3},
journal={Algebraic & Geometric Topology},
publisher={Mathematical Sciences Publishers},
author={Muro, Fernando},
year={2014},
month=Apr,
pages={1489–1539} }
@article{Muro_2015,
title={On determinant functors and $K$-theory},
volume={59},
ISSN={0214-1493},
url={http://dx.doi.org/10.5565/PUBLMAT_59115_07},
DOI={10.5565/publmat_59115_07},
journal={Publicacions Matemàtiques},
publisher={Universitat Autonoma de Barcelona},
author={Muro, F. and Tonks, A. and Witte, M.},
year={2015},
month=Jan,
pages={137–233} }
@misc{jasso2026minimalainftyalgebrasendomorphismscase,
title={Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects},
author={Gustavo Jasso and Fernando Muro},
year={2026},
eprint={2508.18852},
archivePrefix={arXiv},
primaryClass={math.RT},
url={https://arxiv.org/abs/2508.18852},
}
@misc{jasso2026derivedauslanderiyamacorrespondenceii,
title={The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures},
author={Gustavo Jasso and Fernando Muro},
year={2026},
eprint={2509.22625},
archivePrefix={arXiv},
primaryClass={math.RT},
url={https://arxiv.org/abs/2509.22625},
}
@misc{jasso2025obstructiontheoryainfinitybimodules,
title={Obstruction theory for $A$-infinity bimodules},
author={Gustavo Jasso and Fernando Muro},
year={2025},
eprint={2507.17568},
archivePrefix={arXiv},
primaryClass={math.AT},
url={https://arxiv.org/abs/2507.17568},
}
@article{Muro_2023,
title={Massey products for algebras over operads},
volume={51},
ISSN={1532-4125},
url={http://dx.doi.org/10.1080/00927872.2023.2181780},
DOI={10.1080/00927872.2023.2181780},
number={8},
journal={Communications in Algebra},
publisher={Informa UK Limited},
author={Muro, Fernando},
year={2023},
month=Mar,
pages={3298–3313} }
@article{Muro_2019,
title={Enhanced $$A_{\infty }$$-obstruction theory},
volume={15},
ISSN={1512-2891},
url={http://dx.doi.org/10.1007/s40062-019-00245-0},
DOI={10.1007/s40062-019-00245-0},
number={1},
journal={Journal of Homotopy and Related Structures},
publisher={Springer Science and Business Media LLC},
author={Muro, Fernando},
year={2019},
month=July,
pages={61–112} }
@article{Muro_2017,
title={Correction to the articles “Homotopy theory of
nonsymmetric operads”, I–II},
volume={17},
ISSN={1472-2747},
url={http://dx.doi.org/10.2140/agt.2017.17.3837},
DOI={10.2140/agt.2017.17.3837},
number={6},
journal={Algebraic & Geometric Topology},
publisher={Mathematical Sciences Publishers},
author={Muro, Fernando},
year={2017},
month=Oct,
pages={3837–3852} }
@article{Muro_2023,
title={Derived universal Massey products},
volume={25},
ISSN={1532-0081},
url={http://dx.doi.org/10.4310/HHA.2023.v25.n1.a10},
DOI={10.4310/hha.2023.v25.n1.a10},
number={1},
journal={Homology, Homotopy and Applications},
publisher={International Press of Boston},
author={Muro, Fernando},
year={2023},
pages={189–218} }
@article{Muro_2016,
title={Transfinite Adams representability},
volume={292},
ISSN={0001-8708},
url={http://dx.doi.org/10.1016/j.aim.2016.01.009},
DOI={10.1016/j.aim.2016.01.009},
journal={Advances in Mathematics},
publisher={Elsevier BV},
author={Muro, Fernando and Raventós, Oriol},
year={2016},
month=Apr,
pages={111–180} }
@article{Muro_2017,
title={K-theory of derivators revisited},
volume={2},
ISSN={2379-1683},
url={http://dx.doi.org/10.2140/akt.2017.2.303},
DOI={10.2140/akt.2017.2.303},
number={2},
journal={Annals of K-Theory},
publisher={Mathematical Sciences Publishers},
author={Muro, Fernando and Raptis, Georgios},
year={2017},
month=Jan,
pages={303–340} }
@misc{carmona2026modelstructurelocallyconstant,
title={A model structure for locally constant factorization algebras},
author={Victor Carmona and Ramon Flores and Fernando Muro},
year={2026},
eprint={2107.14174},
archivePrefix={arXiv},
primaryClass={math.AT},
url={https://arxiv.org/abs/2107.14174},
}
@article{Guan_2025,
title={Operations on the de Rham cohomology of Poisson and Jacobi manifolds},
volume={31},
ISSN={1420-9020},
url={http://dx.doi.org/10.1007/s00029-025-01087-w},
DOI={10.1007/s00029-025-01087-w},
number={5},
journal={Selecta Mathematica},
publisher={Springer Science and Business Media LLC},
author={Guan, Ai and Muro, Fernando},
year={2025},
month=Oct }
@article{Muro_2019,
title={The first obstructions to enhancing a triangulated category},
volume={296},
ISSN={1432-1823},
url={http://dx.doi.org/10.1007/s00209-019-02438-y},
DOI={10.1007/s00209-019-02438-y},
number={1-2},
journal={Mathematische Zeitschrift},
publisher={Springer Science and Business Media LLC},
author={Muro, Fernando},
year={2019},
month=Dec,
pages={719–759} }
@article{C_rdenas_2005,
title={Proper L–S category, fundamental pro-groups and 2-dimensional proper co-H-spaces},
volume={153},
ISSN={0166-8641},
url={http://dx.doi.org/10.1016/j.topol.2005.01.032},
DOI={10.1016/j.topol.2005.01.032},
number={4},
journal={Topology and its Applications},
publisher={Elsevier BV},
author={Cárdenas, M. and Lasheras, F.F. and Muro, F. and Quintero, A.},
year={2005},
month=Nov,
pages={580–604} }
@article{Flores_2019,
title={Torsion homology and cellular approximation},
volume={19},
ISSN={1472-2747},
url={http://dx.doi.org/10.2140/agt.2019.19.457},
DOI={10.2140/agt.2019.19.457},
number={1},
journal={Algebraic & Geometric Topology},
publisher={Mathematical Sciences Publishers},
author={Flores, Ramón and Muro, Fernando},
year={2019},
month=Feb,
pages={457–476} }
@article{Muro_2016,
title={Cylinders for non-symmetric DG-operads via homological perturbation theory},
volume={220},
ISSN={0022-4049},
url={http://dx.doi.org/10.1016/j.jpaa.2016.02.013},
DOI={10.1016/j.jpaa.2016.02.013},
number={9},
journal={Journal of Pure and Applied Algebra},
publisher={Elsevier BV},
author={Muro, Fernando},
year={2016},
month=Sept,
pages={3248–3281} }
@article{Muro_2011,
title={A note on K-theory and triangulated derivators},
volume={227},
ISSN={0001-8708},
url={http://dx.doi.org/10.1016/j.aim.2011.04.005},
DOI={10.1016/j.aim.2011.04.005},
number={5},
journal={Advances in Mathematics},
publisher={Elsevier BV},
author={Muro, Fernando and Raptis, George},
year={2011},
month=Aug,
pages={1827–1845} }
@article{C_rdenas_2005,
title={The proper L-S category of Whitehead manifolds},
volume={153},
ISSN={0166-8641},
url={http://dx.doi.org/10.1016/j.topol.2005.01.031},
DOI={10.1016/j.topol.2005.01.031},
number={4},
journal={Topology and its Applications},
publisher={Elsevier BV},
author={Cárdenas, M. and Muro, F. and Quintero, A.},
year={2005},
month=Nov,
pages={557–579} }
@article{Ayala_2003,
title={An Elementary Approach to the Projective Dimension in Proper Homotopy Theory},
volume={31},
ISSN={1532-4125},
url={http://dx.doi.org/10.1081/AGB-120024863},
DOI={10.1081/agb-120024863},
number={12},
journal={Communications in Algebra},
publisher={Informa UK Limited},
author={Ayala, R. and Cárdenas, M. and Muro, F. and Quintero, A.},
year={2003},
month=Jan,
pages={5995–6017} }
@article{Muro_2010,
title={Maltsiniotis’s First Conjecture for K1},
ISSN={1687-0247},
url={http://dx.doi.org/10.1093/imrn/rnm153},
DOI={10.1093/imrn/rnm153},
journal={International Mathematics Research Notices},
publisher={Oxford University Press (OUP)},
author={Muro, F.},
year={2010},
month=July }
@article{Maes_2022,
title={Derived homotopy algebras},
volume={153},
ISSN={1473-7124},
url={http://dx.doi.org/10.1017/prm.2022.42},
DOI={10.1017/prm.2022.42},
number={4},
journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
publisher={Cambridge University Press (CUP)},
author={Maes, Jeroen and Muro, Fernando},
year={2022},
month=July,
pages={1198–1243} }
@misc{muro2007triangulatedcategorymodels,
title={A triangulated category without models},
author={Fernando Muro},
year={2007},
eprint={math/0703311},
archivePrefix={arXiv},
primaryClass={math.KT},
url={https://arxiv.org/abs/math/0703311},
}
@misc{muro2006properhomotopytypelocally,
title={On the proper homotopy type of locally compact A^2_n-polyhedra},
author={Fernando Muro},
year={2006},
eprint={math/0605213},
archivePrefix={arXiv},
primaryClass={math.AT},
url={https://arxiv.org/abs/math/0605213},
}
@article{Muro_2004,
title={Representation Theory of some Infinite-dimensional Algebras Arising in Continuously Controlled Algebra and Topology},
volume={33},
ISSN={0920-3036},
url={http://dx.doi.org/10.1007/s10977-004-1837-4},
DOI={10.1007/s10977-004-1837-4},
number={1},
journal={K-Theory},
publisher={Portico},
author={Muro, Fernando},
year={2004},
month=Sept,
pages={23–65} }
