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1. The Only Distributive Law Over the Powerset Monad Is the One You Know
   2026/02/13 by Sergey Goncharov, Dirk Hofmann, Pedro Nora +3 · 1 voice
   Computer Science · Mathematics · #Adjoint functors #Advanced Topology and Set Theory #Algebra over a field #Distributive property #Functor #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #Monad (category theory) #Set (abstract data type) #Uniqueness #cs.LO
2. Anomalies of (1+1)D categorical symmetries
   2023/04/03 by Carolyn Zhang, Zhang, Carolyn, Clay Córdova +1 · 5 citations
   Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Anomaly (physics) #Boundary (topology) #Center (category theory) #Crystallography #FOS: Physical sciences #Functor #Geometry #High Energy Physics - Theory (hep-th) #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Strongly Correlated Electrons (cond-mat.str-el) #Symmetry (geometry)
3. Structured versus Decorated Cospans
   2022/09/01 by John C. Baez, Kenny Courser, Christina Vasilakopoulou · 5 citations
   Mathematics · #Combinatorics #Diagram #Discrete mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Pure mathematics #Symmetric monoidal category
4. Categorical Data Structures for Technical Computing
   2021/06/08 by Evan Patterson, Owen Lynch, James Fairbanks · 2 voices · 5 citations
   Computer Science · Mathematics · #Advanced Database Systems and Queries #Algebraic number #Algebraic structure #Categorical variable #Computer science #Constraint Satisfaction and Optimization #Data structure #Discrete mathematics #Functor #Generalization #Mathematics #Programming language #Pure mathematics #Semantic Web and Ontologies #cs.DB #cs.LO #math.CT
5. The Nakayama functor and its completion for Gorenstein algebras
   2020/10/12 by Srikanth B. Iyengar, Henning Krause, Iyengar, Srikanth B. +1 · 1 citation
   Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Commutative algebra #Context (archaeology) #Derived category #Duality (order theory) #Exact functor #Functor #Homological algebra #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Mathematics #Pure mathematics #Subcategory #math.AC #math.RA #msc:13C60 #msc:13D45 #msc:16E65 #msc:16G30 #msc:18G65
6. D-modules on rigid analytic spaces III: Weak holonomicity and operations
   2019/04/30 by Konstantin Ardakov, Ardakov, Konstantin, Andreas Bode +3 · 2 citations
   Mathematics · #14G22 #32C38 #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic number #Algebraic structures and combinatorial models #Cohomology #Connection (principal bundle) #Dimension (graph theory) #Discrete mathematics #Duality (order theory) #FOS: Mathematics #Functor #Geometry #Holonomic #Homotopy and Cohomology in Algebraic Topology #Integrable system #Mathematical analysis #Mathematics #Number Theory (math.NT) #Physics #Pure mathematics #Representation Theory (math.RT) #Subcategory #Subspace topology #math.AG #math.NT #math.RT #msc:14G22 #msc:32C38
7. Hecke correspondences for smooth moduli spaces of sheaves
   2018/04/10 by Andrei Neguţ, Neguţ, Andrei · 2 citations
   Mathematics · #14D20 #Action (physics) #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Computer science #FOS: Mathematics #Functor #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Quantum Algebra (math.QA) #Space (punctuation) #math.AG #math.QA #msc:14D20
8. Seven Sketches in Compositionality: An Invitation to Applied Category Theory
   2018/03/14 by Brendan Fong, David I. Spivak, David I Spivak +2 · 16 voices · 27 citations
   Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #Art #Artificial intelligence #Categorical variable #Category theory #Computer science #Functor #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Linguistics #Literature #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Model-Driven Software Engineering Techniques #Optics and Image Analysis #Philosophy #Principle of compositionality #Pure mathematics #Topos theory #math.CT #msc:18-01
9. THE GEOMETRY OF BLUEPRINTS PART II: TITS–WEYL MODELS OF ALGEBRAIC GROUPS
   2018/01/01 by Oliver Lorscheid · 1 citation
   Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry #Mathematics #Weyl group #Group (periodic table) #Algebraic group #Morphism #Symplectic geometry #Extension (predicate logic) #Symplectic group #Pure mathematics #Functor #Algebraic number #Combinatorics #Algebra over a field #Mathematical analysis #Physics
10. Floer field theory for tangles
    2015/03/26 by Katrin Wehrheim, Wehrheim, Katrin, Chris Woodward +1 · 2 citations
    Mathematics · #53D40 #Algebraic Geometry and Number Theory #FOS: Mathematics #Functor #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Quantum mechanics #Symplectic Geometry (math.SG) #Symplectic geometry #Triviality #math.SG #msc:53D40
11. Symmetric Powers and Norms of Mackey Functors
    2013/04/20 by John Ullman, Ullman, John · 1 citation
    Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #math.AT
12. The geometry of blueprints. Part II: Tits-Weyl models of algebraic\n groups
    2012/01/05 by Oliver Lorscheid, Lorscheid, Oliver · 2 citations
    Mathematics · #08A99 #14A20 #14L99 #16Y60 #20M14 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Combinatorics #Extension (predicate logic) #FOS: Mathematics #Functor #Group (periodic table) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Morphism #Physics #Pure mathematics #Symplectic geometry #Symplectic group #Weyl group #math.AG #math.GR #msc:08A99 #msc:14A20 #msc:14L99 #msc:16Y60 #msc:20M14
13. Deitmar’s versus Toën-Vaquié’s schemes over \mathbbF₁
    2010/05/31 by Alberto Vezzani · 2 citations
    Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Characterization (materials science) #Coherent sheaf #Commutative property #Equivalence (formal languages) #Equivalence of categories #Functor #Homotopy and Cohomology in Algebraic Topology #Sheaf #math.AG #math.NT
14. Integral transforms and Drinfeld centers in derived algebraic geometry
    2010/04/01 by Dani Ben‐Zvi, John Francis, David Nadler · 2 citations
    Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Hochschild homology #Mathematics #Functor #Pure mathematics #Base change #Tensor product #Cohomology #Derived algebraic geometry #Coherent sheaf #Stack (abstract data type) #Derived category #Product (mathematics) #Algebra over a field #Geometry #Mathematical analysis #Computer science
15. Abstract local cohomology functors
    2010/01/06 by Yuji Yoshino, Yoshino, Yuji, Takeshi Yoshizawa +1 · 1 citation
    Mathematics · #13D09 #13D45 #Adjoint functors #Algebraic structures and combinatorial models #Category Theory (math.CT) #Cohomology #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #De Rham cohomology #Derived functor #Equivariant cohomology #Exact functor #Ext functor #FOS: Mathematics #Finitely-generated abelian group #Functor #Functor category #Grothendieck topology #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Ideal (ethics) #Local cohomology #Mathematics #Motivic cohomology #Pure mathematics #Sheaf cohomology #math.AC #math.CT #msc:13D09 #msc:13D45
16. Representations of Semisimple Lie Algebras in the BGG Category 𝒪
    2008/07/22 by James E. Humphreys · 10 citations
    Mathematics · Psychology · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Functor #Fundamental representation #Homotopy and Cohomology in Algebraic Topology #Index (typography) #Lie algebra #Linguistics #Mathematics #Philosophy #Projective test #Psychology #Pure mathematics #Series (stratigraphy)
17. Sheaves on Artin stacks
    2007/01/27 by Martin Olsson · 2 citations
    Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Morphism #Functor #Mathematics #Pullback #Stack (abstract data type) #Pure mathematics #Coherent sheaf #Mistake #Social connectedness #Algebra over a field #Computer science #Programming language
18. Twisted Fourier-Mukai functors
    2006/05/09 by Alberto Canonaco, Canonaco, Alberto, Paolo Stellari +1 · 5 citations
    Computer Science · Mathematics · #14F22 #18E10 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functor #Mathematical Dynamics and Fractals #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #advanced mathematical theories #math.AG #msc:14F22 #msc:18E10 #msc:18E30
19. Almost-commuting variety, D-modules, and Cherednik Algebras
    2004/09/15 by Wee Liang Gan, Victor Ginzburg, Gan, Wee Liang +1 · 5 citations
    Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics #FOS: Mathematics #Functor #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Intersection (aeronautics) #Mathematics #Polynomial and algebraic computation #Pure mathematics #Quantum Algebra (math.QA) #Rank (graph theory) #Representation Theory (math.RT) #Subvariety #Type (biology) #Variety (cybernetics) #math.AG #math.QA #math.RT
20. Local Homology and Cohomology on Schemes
    1995/03/30 by Leovigildo Alonso, Alonso, Leovigildo, Ana Jeremías +3 · 1 citation
    Mathematics · #14B15 #14B20 #14Fxx #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Coherent sheaf #Cohomology #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Duality (order theory) #FOS: Mathematics #Finitely-generated abelian group #Functor #Generalization #Local cohomology #Mathematical analysis #Mathematics #Poincaré duality #Pure mathematics #Sheaf #alg-geom #math.AC #math.AG #msc:14B15 #msc:14B20 #msc:14Fxx
21. Homotopy Theories and Model Categories
    1995/01/01 by W. G. Dwyer, W.G. Dwyer, J. Spalinski +1 · 12 citations
    Biochemistry, Genetics and Molecular Biology · Mathematics · #Algebraic structures and combinatorial models #Artificial intelligence #Axiom #Category of sets #Class (philosophy) #Computer science #Concrete category #Context (archaeology) #Enriched category #Epistemology #Functor #Geometry #Higher category theory #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Interpretation (philosophy) #Mathematics #Model category #Morphism #Pure mathematics #Simple (philosophy) #Sphingolipid Metabolism and Signaling
22. Deriving DG categories
    1994/01/01 by Bernhard Keller · 14 citations
    Mathematics · #2-category #Abelian category #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Biproduct #Category of groups #Category theory #Context (archaeology) #Derived category #Formalism (music) #Functor #Homological algebra #Homotopy and Cohomology in Algebraic Topology #Mathematics #Morita therapy #Pure mathematics #Triangulated category