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[parent] index of categories (Topic)

Index of categories

The following is a contributed listing, or Index of Categories:
  1. Category of sets, $Set$ or $Ens$
  2. Cartesian closed category, or $Cc$ -category; an example is $Set$
  3. Category of molecular sets: a $Cc$ -category
  4. Category of organismic sets: a model subcategory of $Set$
  5. Category of $(M,R)$ -systems: a $Cc$ -category
  6. Dual category
  7. Double dual category, $V^{**}$
  8. Category of dynamical systems
  9. Abelian categories: Grothendieck category, category of Abelian groups, category of sheaves of abelian groups, category of reversible automata $\mathcal{A}_R$
  10. Complete and cocomplete categories
  11. Comma category
  12. $C_1$ -category
  13. $C_2$ -category
  14. $C_3$ -category
  15. $Ab5$ -category
  16. Category of additive fractions
  17. Category of fractions
  18. Quotient category
  19. Grassmann category
  20. Category of groups
  21. Category of crossed modules of groups
  22. Category of crossed modules of algebroids
  23. Category of matrices
  24. Category of Abelian (or commutative) groups
  25. Category of Polish groups
  26. Category of Lie 2-groups, (also an example of internal category)
  27. Categorical groups
  28. Internal categories
  29. Monoidal category: a. symmetric, b. braided, c.closed
  30. Category of semigroups
  31. Category of rings
  32. Category of modules
  33. Category of crossed modules
  34. Category of crossed complexes
  35. Groupoid category
  36. Category of topological spaces
  37. Homotopy category
  38. Category of sheaves of Abelian groups
  39. Category of Riemannian manifolds
  40. Borel category
  41. Category of graphs: category of reflexive (or directed) graphs
  42. Category of paths on a graph
  43. Category of hypergraphs
  44. Category of groupoids, Groupoid category
  45. Category of topological groupoids
  46. Category of Borel groupoids
  47. Cohomology of small categories
  48. Category of C*-algebras
  49. $2-C^*$ -category,${\mathcal{C}^*}_2$
  50. Category of H $*$ -algebras
  51. Category of Hilbert spaces
  52. Category of automata
  53. Category of quantum automata
  54. Algebraic categories
  55. Category of logic algebras
  56. Category of lattices
  57. Category of Boolean algebras
  58. Algebraic category of \Lukasiewicz-Moisil, $LM_n$ -algebras
  59. Category of Heyting algebras
  60. Category of topoi
  61. Category of genetic nets
  62. Category of quantum logic algebras
  63. R-category
  64. Category of algebroids
  65. Category of double algebroids
  66. Grassmann-Hopf algebroid category
  67. Topological category
  68. Galois category
  69. Subcategory
  70. Internal category
  71. Groupoid groups
  72. Groupoid category
  73. Fibered categories
  74. Non-Abelian categories
  75. Category of diagrams
  76. Functor category, or category of functors and functorial morphisms (natural transformations)
  77. Category of small categories
  78. Category of categories, super-category
  79. Supercategory
  80. Meta-category
  81. Category of functors, (or Functor category)
  82. 2-category; specific examples are: a Lie 2-group, Abelian 2-category, 2-category of commutative (or Abelian) groupoids.
  83. Double category
  84. n-category
  85. Double groupoid category



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See Also: index of category theory, category, category theory, topics in algebraic topology, $C_1$-category, $C_2$-category, $C_3$-category, Grothendieck category, closed monoidal category, proof that abelian groups form an abelian category, examples of abelian categories, Cartesian closed category, groupoid C*-dynamical system, dynamical system, 2-category, axioms of metacategories and supercategories, categorical algebra, categorical quantum logics as quantum LM-algebraic logic, categories and supercategories in relational biology, category of $(M,R)$--systems, category of automata, category of Borel groupoids, category of Borel spaces, category of C*-algebras, category of Hilbert spaces, category of H $*$ -algebras, category of molecular sets, category of quantum automata, category of Riemannian manifolds, duality in mathematics, examples of functor categories, natural equivalence of categories, natural equivalence of $C_G$ and $C_M$ categories, categories and QAT bibliography in algebraic topology, Grassmann-Hopf algebroid categories and Grassmann categories, category of paths on a graph, category of pointed topological spaces, quantum fundamental groupoid, category of sets, category of small categories, complete category, cohomology of small categories, supercomputers

Also defines:  $Cc$-category
Keywords:  `all' types of categories with specific examples

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Cross-references: double groupoid, n-category, double category, 2-category, meta-category, supercategory, category of categories, category of small categories, natural transformations, functorial morphisms, category of functors, functor category, diagrams, non-Abelian, groupoid, Grassmann-Hopf algebroid category, R-category, algebras, quantum logic, category of genetic nets, topoi, Heyting algebras, Boolean algebras, category of logic algebras, algebraic categories, category of quantum automata, category of automata, category of Hilbert spaces, category of C*-algebras, cohomology of small categories, category of Borel groupoids, category of groupoids, hypergraphs, graphs, Reflexive, category of graphs, category of Riemannian manifolds, homotopy category, topological spaces, groupoid category, complexes, rings, semigroups, symmetric, monoidal category, categorical, internal category, Polish groups, commutative, abelian, category of matrices, modules, groups, Grassmann category, quotient category, category of fractions, category of additive fractions, comma category, cocomplete categories, complete, category of reversible automata, abelian groups, sheaves, Grothendieck category, abelian categories, dynamical systems, dual category, subcategory, organismic sets, category, category of molecular sets, category of sets
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This is version 56 of index of categories, born on 2008-10-21, modified 2009-02-01.
Object id is 11196, canonical name is IndexOfCategories.
Accessed 1295 times total.

Classification:
AMS MSC: 18-00 (Category theory; homological algebra :: General reference works )
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