bibliography for axiomatics and mathematics foundations in categories

bibliography for axiomatics and mathematics foundations in categories

0.1

A Bibliography for Axiomatic Theories and Categorical Foundations of Mathematical Physics and Mathematics

0.1.1

a. Foundations of Mathematics, Logics and
Formal Logics (

http://planetmath.org/AnalyticsAndOntologyFormalLogics

):
Axiomatics, Categories, Topoi and Higher Dimensional Algebra (

http://planetmath.org/HigherDimensionalAlgebraHDA

)

References

1

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, 3, 209–237.

2

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3

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n

-

Categories

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16

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35

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(M,R)

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.

8

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9

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10

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Monoidal

Globular Categories as a Natural Environment for the Theory of Weak n-Categories., Advances in Mathematics, 136, 39–103.

11

Bell, J. L. 1981. Category Theory and the

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,

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12

Bell, J. L., 1982. Categories, Toposes and Sets,

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13

Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite

Forcing

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14

Blass, A. and Scedrov, A., 1989, Freyd’s Model for the Independence of the

Axiom of Choice

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15

Blass, A. and Scedrov, A., 1992.

Complete

Topoi Representing Models of

Set Theory

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16

Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5–29.

17

Blute, R. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science

18

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Proceedings of the International Conference on Theoretical Neurobiology

, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre,

Conference Proceedings

1

: 80-92.

19

Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The

homotopy double groupoid

of a

Hausdorff space

.,

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10

, 71-93.

20

Brown, R. and Spencer, C.B.: 1976,

Double groupoids

and crossed modules,

Cah. Top. Géom. Diff.

17

, 343-362.

21

Brown R, Razak Salleh A (1999) Free crossed

resolutions

of groups and

presentations

of modules of

identities

among relations.

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,

2

: 25–61.

22

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Trans. Amer. Math. Soc.

80

: 1-34.

23

Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes,

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179

, 291-317.

24

Bunge, M., 1984, Toposes in Logic and Logic in Toposes,

Topoi

, 3, no. 1, 13-22.

25

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,

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26

Ehresmann, C.: 1965,

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27

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Cahiers de Topologie et Geometrie Differentielle

8

: 1-7.

.1.2

b. Universal Algebra, Classes of Algebraic Structures and Homology; Abelian and
Non-Abelian theories (

http://planetmath.org/NonAbelianTheories

); Algebraic
Geometry and Noncommutative Geometry (

http://planetmath.org/NoncommutativeGeometry

)

.

References

28

Brown, R., Higgins, P. J. and R. Sivera,: 2007,

Non-Abelian

Algebraic Topology

,

http://www.bangor.ac.uk/ mas010/nonab-t/partI010604.pdf

vol.I pdf doc.;

http://

planetmath

.org/?op=getobj&from=lec&id=75

Review of Part I and full

contents

PDF doc.

29

R. Brown. 2008.

Higher Dimensional Algebra Preprint as pdf and ps docs. at arXiv:math/0212274v6 [math.AT]

30

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,

71

: 273-286.

31

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32

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33

M. Chaician and A. Demichev. 1996.

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to

Quantum Groups

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34

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35

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36

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non-commutative

.

,
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37

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38

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39

Dixmier, J., 1981,

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40

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41

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42

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43

Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables,

Coll. Géom. Diff. Glob.

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44

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45

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, edited and commented by Andrée Ehresmann.

46

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.,

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43

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47

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48

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49

Eilenberg, S. & MacLane, S., 1942,

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and

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,

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50

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51

Eilenberg, S.: 1960. Abstract description of some basic

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52

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53

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54

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W

∞

algebra and Grassmannian solitons in multicomponent Hall systems, (at arXiv:hep–th/0209198).

55

Freyd, P., 2002, Cartesian Logic,

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, 278, no. 1–2, 3–21.

56

Freyd, P., Friedman, H. & Scedrov, A., 1987, Lindembaum Algebras of Intuitionistic Theories and

Free Categories

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, 35, 2, 167–172.

57

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58

Gabriel, P.: 1962, Des catégories abéliennes,

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59

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60

Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes
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61

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,

64

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62

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Imbedding

of

Normed Rings

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63

Ghilardi, S. & Zawadowski, M., 2002,

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Model Completions

: A Categorical Approach to Nonclassical

Propositional Logics

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64

Ghilardi, S., 1989,

Presheaf

Semantics

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65

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,

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66

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Thèse.

, Univ. Lille, 1971.

67

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68

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in non-commutative

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,

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,

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69

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70

Gray, C. W.: 1965. Sheaves with values in a category.,

Topology

, 3: 1-18.

71

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72

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,

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73

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Publ. Inst. des Hautes Etudes de Science

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4

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74

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75

Hardie, K.A. K.H. Kamps and R.W. Kieboom, A

homotopy

2-groupoid of a Hausdorff space,

Applied Cat. Structures

8 (2000), 209-234.

76

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The

Logical Foundations

of Mathematics

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77

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Abelian categories

.,

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68

: 484-525.

78

Heller, A. and K. A. Rowe.:1962, On the category of sheaves.,

Amer J. Math.

84

: 205-216.

79

Hellman, G., 2003, ”Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.

80

Hermida, C. & Makkai, M. & Power, J., 2000, On Weak Higher-dimensional Categories I, Journal of Pure and Applied Algebra, 154, no. 1-3, 221–246.

81

Hermida, C. & Makkai, M. & Power, J., 2001, On Weak Higher-dimensional Categories II, Journal of Pure and Applied Algebra, 157, no. 2-3, 247–277.

82

Hermida, C. & Makkai, M. & Power, J., 2002, On Weak Higher-dimensional Categories III, Journal of Pure and Applied Algebra, 166, no. 1-2, 83–104.

83

Higgins, P. J.: 2005,

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Reprints in
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, No. 7: 1-195.

84

Higgins, Philip J. Thin elements and

commutative

shells in cubical

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85

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London Mathematical Society

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86

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, 110, Amsterdam: North Holland, 165–216.

87

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Complete Category

,

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, 40, no. 2, 135–165.

88

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89

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, 114, no. 1–3, 43–78.

90

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.,

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91

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92

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93

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Conditions Related to De Morgan’s Law, Applications of Sheaves

, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.

94

Johnstone, P. T., 1981,

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’s

Theorem

without the Axiom of Choice,

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95

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96

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Aspects of Topology

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97

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98

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Fundamental
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99

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100

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101

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,

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102

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103

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104

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,

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105

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,

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106

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107

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108

Lambek, J., 1969,

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, Category Theory, Homology Theory and their Applications I

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109

Lambek, J., 1972,

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110

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111

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112

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Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics

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113

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114

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115

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116

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117

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118

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119

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120

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121

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122

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123

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124

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125

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126

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127

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128

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135

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136

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137

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145

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146

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147

MacLane, S., 1986,

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148

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149

MacLane, S., 1989, The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory, in

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150

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151

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152

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153

MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag.

154

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155

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156

Makkai, M. & Paré, R., 1989,

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157

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158

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159

Makkei, M. & Reyes, G., 1995, Completeness Results for Intuitionistic and

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160

Marquis, J.-P., 1993, Russell’s Logicism and Categorical Logicisms, in

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161

Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations.,

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Title

bibliography for axiomatics and mathematics foundations in categories

Canonical name

BibliographyForAxiomaticsAndMathematicsFoundationsInCategories

Date of creation

2013-03-22 18:19:31

Last modified on

2013-03-22 18:19:31

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bci1 (20947)

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bci1 (20947)

Numerical id

42

Author

bci1 (20947)

Entry type

Bibliography

Classification

msc 55U99

Classification

msc 03B50

Classification

msc 18A05

Classification

msc 18-00

Classification

msc 03-00

Classification

msc 00A15

Synonym

metamathematics

Synonym

mathematical foundations

Synonym

axiomatics and formal logics

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BibliographyForMathematicalPhysicsFoundationsAxiomaticsAndCategories

Related topic

NonAbelianTheories

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TopicEntryOnMiscellaneousMathematics

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