Work/Publications by Subject

Algebraic Theories & Algebraic Categories

1. Functorial Semantics of Algebraic Theories, 
Proceedings of the National Academy of Science 50, No. 5 (November 1963), 869-872. Reprint PDF

3. Algebraic Theories, Algebraic Categories, and Algebraic Functors, 
Theory of Models; North-Holland, Amsterdam (1965), 413-418. PDF

6. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories, 
Springer Lecture Notes in Mathematics No. 61, Springer-Verlag (1968), 41-61. Reprint PDF

19. Review of P. M. Cohn’s Universal Algebra, 2nd Edition, 
American Scientist (May-June 1982), p. 329. PDF

42. (with J. Adamek and J. Rosicky) How algebraic is algebra? 
Theory and Applications of Categories, online publication, vol. 8, (2001), 253-283. (link)

46. (with J. Adamek and J. Rosicky) On the duality between varieties and algebraic theories,
Algebra Universalis, (2003) 35-49. PDF

53. Reprint with new author commentary on both Functorial Semantics of Algebraic Theories (Thesis 1963) and Some algebraic problems in the context of functorial semantics of algebraic theories (1968) 
Reprints in Theory and Applications of Categories, online publication, No. 5 (2004) pp 1-121 (link)

65. Foreword to 
Algebraic Theories by J. Adamek, J. Rosicky and E. M. Vitale, Cambridge Tracts in Mathematics 184, (2012). PDF

68. Birkhoff’s Theorem from a geometric perspective: A simple example 
Categories and General Algebraic Structures with Apllications Vol. 4, no. 1, (2016), pp. 1-7. (pdf)

Topos Theory

11. Quantifiers and Sheaves, 
Proceedings of the International Congress on Mathematics, (Nice 1970), Gauthier-Villars (1971) 329-334. PDF

12. Introduction to the Proceedings of the Halifax Conference, Toposes, Algebraic Geometry and Logic, 
Springer Lecture Notes in Mathematics No. 274, Springer-Verlag (1972), 1-12 PDF

14. Continuously Variable Sets: Algebraic Geometry = Geometric Logic, 
Proceedings of the Logic Colloquium, Bristol (1973), North Holland (1975), 135-157. PDF

15. Introduction to Part I of Model Theory and Topoi, 
Springer Lecture Notes in Mathematics No.445, Springer-Verlag (1975), 3-14. PDF

16. Variable Quantities and Variable Structures in Topoi, 
Algebra, Topology and Category Theory, A Collection in Honor of Samuel Eilenberg, Academic Press (1976), 101-131. PDF

23. Categories of Spaces may not be Generalized Spaces, as Exemplified by Directed Graphs, 
Revista Colombiana de Matemáticas XX (1986), 179-185. Reprint

25. Qualitative Distinctions between some Toposes of Generalized Graphs, Proceedings of AMS Boulder 1987 Symposium on Categories in Computer Science and Logic,
Contemporary Mathematics 92 (1989), 261-299. PDF

26. (with G. M. Kelly) On the Complete Lattice of Essential Localizations, 
Bulletin Société Mathématique de Belgique XLI (1989), 289-319. PDF

29. Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes, 
Category Theory, Proceedings Como 1990. Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) 279-281. PDF

30. Some Thoughts on the Future of Category Theory, 
Category Theory, Proceedings Como 1990. Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) 1-13. PDF

33. Cohesive Toposes and Cantor’s “lauter Einsen”, 
Philosophia Mathematica, The Canadian Society for History and Philosophy of Mathematics, Series III, Vol. 2 (1994), 5-15. PDF

34. Theory of Mathematical Categories,
(1995) Encyclopedia article, publication canceled. Italian version below at #39.

39. Categorie e Spazio: Un Profilo, 
Lettera matematica PRISTEM 31, Springer, Italy, (1999), 35-50. [Reprinted in La Mathematica  a cura di Bartocci, Claudio,  Giulio Einaudi editore (2010) vol. 4,  107-135.] PDF

40. Comments on the Development of Topos Theory, 
Development of Mathematics 1950-2000, J.-P. Pier (Ed) Birkhäuser Verlag, Basel, (2000), 715-734. Reprint PDF

49. (with J. Adamek and J. Rosicky) Continuous Categories Revisited, 
Theory and Applications of Categories, online publication, vol. 11, (2003), 252-282.  (link)

56. Reprint with new author commentary Categories of Spaces may not be Generalized Spaces, as Exemplified by Directed Graphs(1986) 
Reprints in Theory and Applications of Categories, online publication, No. 9, (2005), pp. 1-7 (link)

60. Review of Synthetic Differential Geometry Second Edition
by Kock, Anders. SIAM Review, Vol 49, 349-350, (2007). [on page 349 there is a slip: K.T. Chen’s proposed category certainly has smooth function spaces]. PDF

61. Axiomatic Cohesion 
Theory and Applications of Categories, online publication, Special volume from the CT2006 Conference at Whitepoint Nova Scotia, vol 19, (2007), 41-49. (link) PDF

62. Core Varieties, Extensivity, and Rig Geometry
Theory and Applications of Categories, online publication,  vol 20, (2008), 497-503. (link)

66. Reprint with new author commentary  
Comments on the Development of Topos Theory (2000) Reprints in Theory and Applications of Categories, online publication, No. 24, (2014), pp. 1-22 (link)

67. (with M. Menni) Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness
Theory and Applications of Categories, online publication, vol. 30, (2015), No. 26, pp 909-932. (link)

68. Birkhoff”s Theorem from a geometric perspective: A simple example 
Categories and General Algebraic Structures with Apllications Vol. 4, no. 1, (2016), pp. 1-7. (pdf)

Philosophy

9. Adjointness in Foundations, 
Dialectica 23 (1969), 281-296. Reprint

30. Some Thoughts on the Future of Category Theory, 
Category Theory, Proceedings Como 1990. Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) 1-13. PDF

31. Categories of Space and of Quantity, International Symposium on Structures in Mathematical Theories (1990),
San Sebastian, Spain; The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, DeGruyter, Berlin (1992), 14-30. PDF

32. Tools for the Advancement of Objective Logic: Closed Categories and Toposes, J. Macnamara & G. E. Reyes (Eds). 
The Logical Foundations of Cognition, Oxford University Press (1994), 43-56. PDF

33. Cohesive Toposes and Cantor’s “lauter Einsen”, 
Philosophia Mathematica, The Canadian Society for History and Philosophy of Mathematics, Series III, Vol. 2 (1994), 5-15. PDF

36. Unity and Identity of Opposites in Calculus and Physics, Proceedings of ECCT 1994 Tours Conference, 
Applied Categorical Structures, 4: 167-174 Kluwer Academic Publishers, 1996. PDF

38. Kinship and Mathematical Categories, 
Language, Logic, and Conceptual Representation (in memory of John Macnamara): 411-425, MIT Press 1999, Ed. P. Bloom, R. Jackendoff, and K. Wynn. PDF

39. Categorie e Spazio: Un Profilo, 
Lettera matematica PRISTEM 31, Springer, Italy, (1999), 35-50. [Reprinted in La Mathematica  a cura di Bartocci, Claudio,  Giulio Einaudi editore (2010) vol. 4,  107-135.] PDF

40. Comments on the Development of Topos Theory, 
Development of Mathematics 1950-2000, Ed. by J-P Pier, Birkhauser Verlag, Basel, 2000. Reprint PDF

47. Foundations and Applications: Axiomatization and Education, 
The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), 213-224. PDF

57. Long version with new commentary by the author and by Colin McLarty: An Elementary theory of the category of sets (1964) (long version)
Reprints in Theory and Applications of Categories, online publication, No. 11, (2005), pp. 1-35 (link)

58. Reprint with new author commentary Diagonal Arguments and Cartesian Closed Categories (1969)
Reprints in Theory and Applications of Categories, online publication, No. 15, (2006), pp. 1-13. (link)

59. Reprint with new author commentary Adjointness in Foundations (1969)
Reprints in Theory and Applications of Categories, online publication, No. 16, (2006), 1-16. (link)

64. Euler’s Continuum Functorially Vindicated,
Logic, Mathematics, Philosophy: Vintage Enthusiasms, Essays in Honour of John L. Bell, D. DeVidi et al. (Eds), Western Ontario Series in Philosophy of Science 75, (2011). PDF

Logic

4. Functorial Semantics of Elementary Theories, 
Journal of Symbolic Logic, Abstract, Vol. 31 (1966), 294-295. PDF

7. Ordinal Sums and Equational Doctrines, 
Springer Lecture Notes in Mathematics No. 80, Springer-Verlag (1969), 141-155. PDF

8. Diagonal Arguments and Cartesian Closed Categories, 
Springer Lecture Notes in Mathematics No. 92, Springer-Verlag (1969), 134-145. Reprint

10. Equality in Hyperdoctrines and Comprehension Schema as an Adjoint Functor, 
Proceedings of the American Mathematical Society Symposium on Pure Mathematics XVII (1970), 1-14. PDF

13. Metric Spaces, Generalized Logic and Closed Categories, 
Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166. Reprint

15. Introduction to Part I of Model Theory and Topoi, 
Springer Lecture Notes in Mathematics No.445, Springer-Verlag (1975), 3-14. PDF

29. Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes,
Category Theory, Proceedings Como 1990. Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) 279-281. PDF

35. Adjoints in and among Bicategories, Proceedings of the 1994 Siena Conference in Memory of Roberto Magari. 
Logic & Algebra, Lecture Notes in Pure and Applied Algebra 180: 181-189, Ed. Ursini/Aglianò, Marcel Dekker, Inc. Basel, New York, 1996. PDF

47. Foundations and Applications: Axiomatization and Education, 
The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), 213-224. PDF

51. Left and Right Adjoint Operations on Spaces and Data Types, 
For Dana Scott’s Seventieth Birthday, Copenhagen 2002, Theoretical Computer Science, Elsevier, vol 316/1-3, (2004) 105-111. PDF

Physics

17. Categorical Dynamics in Proceedings of Aarhus May 1978 Open House on Topos Theoretic Methods in Geometry (1979), Aarhus/Denmark. PDF

18. Toward the Description in a Smooth Topos of the Dynamically Possible Motions and Deformations of a Continuous Body, Cahiers de Topologie et Géométrie Différentielle Catégorique XXI (1980), 337-392. PDF

20. State Categories, Closed Categories, and the Existence of Semicontinuous Entropy Functions – IMA Research Report #86, University of Minnesota (1986). PDF

21. Functorial Remarks on the General Concept of Chaos – IMA Research Report #87, University of Minnesota (1986). PDF

22. Introduction to Categories in Continuum Physics, Springer Lecture Notes in Mathematics No. 1174, Springer-Verlag (1986). PDF

36. Unity and Identity of Opposites in Calculus and Physics, Proceedings of ECCT 1994 Tours Conference, Applied Categorical Structures, 4: 167-174 Kluwer Academic Publishers, 1996. PDF

41. Volterra’s functionals and covariant cohesion of space, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Numero 64, 2000, Ed. R. Betti and F.W. Lawvere. PDF

44. Categorical algebra for continuum micro physics , Journal of Pure and Applied Algebra 175 (2002) 267-287. PDF

Didactic

24. Taking Categories Seriously, Revista Colombiana de Matemáticas XX (1986), 147-178. Reprint

34. Theory of Mathematical Categories, (1995) Encyclopedia article, publication delayed.

36. Unity and Identity of Opposites in Calculus and Physics, Proceedings of ECCT 1994 Tours Conference, Applied Categorical Structures, 4: 167-174 Kluwer Academic Publishers, 1996. PDF

39. Categorie e Spazio: Un Profilo, Lettera matematica PRISTEM 31: 35-50, Springer, Italy, 1999. PDF

47. Foundations and Applications: Axiomatization and Education, The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), 213-224.PDF

50. Concetti fondazionali espliciti nell’insegnamento della matematica, Matematica e filosofia: il problema dei fondamenti oggi PRISTEM/Storia 14-15 a cura di Albeverio, Sergio e Minazzi, Fabio. Atti del Convegno di Mendrisio, 16 novembre 2001. [Interdisciplinary Encounter on the Problem of Foundations of Mathematics]).

50a. English translation: Explicit foundational concepts in the teaching of mathematics in Filsofia, scienza e bioetica nel dibattito contemporaneo a cura di Minazzi, Fabio, Instituto Poligrafico e Zecca dello Stato, Roma (2007). PDF

55. Reprint with new author commentary, Taking Categories Seriously (1986) Reprints in Theory and Applications of Categories, online publication, No. 8, (2005), pp. 1-24 (link)

Computer Science

25. Qualitative Distinctions between some Toposes of Generalized Graphs, Proceedings of AMS Boulder 1987 Symposium on Categories in Computer Science and Logic, Contemporary Mathematics 92 (1989), 261-299. PDF

27. Display of Graphics and their Applications, as Exemplified by 2-Categories and the Hegelian “Taco”, Proceedings of the First International Conference on Algebraic Methodology and Software Technology, The University of Iowa, (1989). PDF

28. More on Graphic Toposes, Proceedings of the 1989 Bangor Category Theory Meeting, Cahiers de Topologie et Géométrie Différentielle Catégorique XXXII – 1 (1991), 5-10. PDF

51. Left and Right Adjoint Operations on Spaces and Data Types, For Dana Scott’s Seventieth Birthday, Copenhagen 2002, Theoretical Computer Science, Elsevier, vol 316/1-3, (2004) 105-111. PDF

54. Functorial Concepts of Complexity for Finite Automata, (in honor of Aurelio Carboni’s 60th Birthday) Theory and Applications of Categories, online publication, vol 13, (2005) (link).

63. (with M. Menni) The Hopf Algebra of Möbius Intervals Theory and Applications of Categories, online publication, vol. 24, (2010), 221-265. (link)

History

33. Cohesive Toposes and Cantor’s “lauter Einsen”, Philosophia Mathematica, The Canadian Society for History and Philosophy of Mathematics, Series III, Vol. 2 (1994), 5-15. PDF

37. Grassmann’s Dialectics and Category Theory, Hermann Günther Grassmann (1809-1877): Visionary Mathematician, Scientist and Neohumanist Scholar, Proceedings of the 1994 Conference to commemorate 150 years of Grassmann’s “Ausdehnungslehre”, Gert Schubring (Ed), Boston Studies in the Philosophy of Science, 187: 255-264, Kluwer Academic Publishers, (1996). PDF

40. Comments on the Development of Topos Theory, Development of Mathematics 1950-2000, Ed. by J-P Pier, Birkhauser Verlag, Basel, 2000. Reprint PDF

41.Volterra’s functionals and covariant cohesion of space, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Numero 64, 2000, Ed. R. Betti and F.W. Lawvere. PDF

48. Incontro con Ludovico Geymonat, anno 1977, Filosofia, scienza e vita civile nel pensiero di Ludovico Geymonat (a cura di Minazzi, Fabio), La città del sole, Napoli, (2003), 181-185. [English: Encounter with Ludovico Geymonat in 1977.] PDF

52. Essay Review of:

A new branch of mathematics, “The Ausdehnungslehre of 1844”, and other works by Hermann Günther Grassmann, translated by Lloyd C. Kannenberg, with foreword by Albert C. Lewis, Open Court Publishing Company, (1995).

and of

Extension Theory, “The Ausdehnungslehre of 1862” by Hermann Günther Grassmann, translated and with a foreword and notes by Lloyd C. Kannenberg, History of Mathematics, 19, American Mathematical Society and London Mathematical Society, (2000).

Historia Mathematica, vol. 32, (2005), pp. 101-106 (link) PDF

Anthropology

38. Kinship and Mathematical Categories, (in memory of John Macnamara), Language, Logic, and Conceptual Representation, P. Bloom, R. Jackendoff, and K. Wynn (Eds), MIT Press, (1999), 411-425. PDF