1. Functorial Semantics of Algebraic Theories,
Proceedings of the National Academy of Science 50, No. 5 (November 1963), 869-872. Reprint
2. Elementary Theory of the Category of Sets,
Proceedings of the National Academy of Science 52, No. 6 (December 1964), 1506-1511. Reprint
3. Algebraic Theories, Algebraic Categories, and Algebraic Functors,
Theory of Models; North-Holland, Amsterdam (1965), 413-418. PDF
4. Functorial Semantics of Elementary Theories,
Journal of Symbolic Logic, Abstract, Vol. 31 (1966), 294-295. PDF
5. The Category of Categories as a Foundation for Mathematics,
La Jolla Conference on Categorical Algebra, Springer-Verlag (1966), 1-20. 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
7. Ordinal Sums and Equational Doctrines,
Springer Lecture Notes in Mathematics No. 80, Springer-Verlag (1969), 141-155. PDF or see Reprint of full volume.
8. Diagonal Arguments and Cartesian Closed Categories,
Springer Lecture Notes in Mathematics No. 92, Springer-Verlag (1969), 134-145. Reprint
9. Adjointness in Foundations,
Dialectica 23 (1969), 281-296. 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
11. Quantifiers and Sheaves,
Proceedings of the International Congress on Mathematics, Nice 1970, Gauthier-Villars (1971) 329-334. PDF
12. Introduction to Toposes, Algebraic Geometry and Logic
Proceedings of the Halifax Conference Springer Lecture Notes in Mathematics No. 274, Springer-Verlag (1972), 1-12 PDF
13. Metric Spaces, Generalized Logic and Closed Categories,
Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166. Reprint
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, F.W. Lawvere, C. Maurer, G. Wraith (Eds), 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, A. Heller, M. Tierney (Eds), Academic Press (1976), 101-131. PDF
17. Categorical Dynamics,
Open House on Topos Theoretic Methods in Geometry Proceedings of Aarhus May 1978 (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
19. Review of P. M. Cohn’s Universal Algebra,
2nd Edition, American Scientist (May-June 1982), 329. 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
23. Categories of Spaces may not be Generalized Spaces, as Exemplified by Directed Graphs
Revista Colombiana de Matemáticas XX (1986), 179-185. Reprint
24. Taking Categories Seriously
Revista Colombiana de Matemáticas XX (1986), 147-178. Reprint
25. Qualitative Distinctions between some Toposes of Generalized Graphs,
Contemporary Mathematics 92, Proceedings of AMS Boulder 1987 Symposium on Categories in Computer Science and Logic, J. Gray, A. Scedrov (Eds), (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
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
29. Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes,
Category Theory, Proceedings Como 1990, A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). 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. A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) 1-13. PDF
31. Categories of Space and of Quantity,
The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, International Symposium on Structures in Mathematical Theories (1990), San Sebastian, Spain; DeGruyter, Berlin (1992), 14-30. PDF
32. Tools for the Advancement of Objective Logic: Closed Categories and Toposes,
The Logical Foundations of Cognition, J. Macnamara, G. E. Reyes (Eds). 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
34. Theory of Mathematical Categories,
(1995) Encyclopedia article, publication canceled. Italian version below at #39.
35. Adjoints in and among Bicategories,
Logic & Algebra, Proceedings of the 1994 Siena Conference in Memory of Roberto Magari. Lecture Notes in Pure and Applied Algebra 180: 181-189, Ed. Ursini/Aglianò, Marcel Dekker, Inc. Basel, New York, (1996). 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
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
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
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
41. Volterra’s functionals and covariant cohesion of space,
Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 64, R. Betti, F. W. Lawvere (Eds), (2000), 201-214. 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)
43. Linearization of Graphic Toposes via Coxeter Groups,
Journal of Pure and Applied Algebra, vol. 168, (2002), 425-436. PDF
44. Categorical algebra for continuum microphysics,
Journal of Pure and Applied algebra 175, (2002), 267-287. PDF
45. Enriched Categories in the Logic of Geometry and Analysis,
Reprint with new author commentary of Metric Spaces, Generalized Logic, and Closed Categories (1973),
Reprints in Theory and Applications of Categories, online publication, No. 1, (2002), 1-39. (link)
46. (with J. Adamek and J. Rosicky) On the duality between varieties and algebraic theories,
Algebra Universalis, (2003), 35-49. PDF
47. Foundations and Applications: Axiomatization and Education,
The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), 213-224. 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
49. (with J. Adamek and J. Rosicky) Continuous Categories Revisited,
Theory and Applications of Categories, online publication, vol. 11, (2003), 252-282. 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
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
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
53. Reprint with new author commentary of 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)
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).
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)
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)
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)
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)
63. (with M. Menni) The Hopf Algebra of Möbius Intervals
Theory and Applications of Categories, online publication, vol. 24, (2010), 221-265. (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
65. Foreword to Algebraic Theories by J. Adamek, J. Rosicky and E. M. Vitale,
Cambridge Tracts in Mathematics 184, (2012). PDF
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)
69. Everyday Physics of Extended Bodies, or Why Functionals Need Analyzing
Categories and General Algebraic Structures with Application, Vol. 6, Special Issue on the Occasion of Banaschewski’s 90th Birthday (I), (2017) 9-19. (pdf)
70. Toposes generated by codiscrete objects in combinatorial topology and functional analysis
This article is the summary of the notes for the colloquium lectures at North Ryde,NSW, Australia (1988). Reprints in Theory and Applications of Categories, 27 (2021) pp. 1-11 (pdf)
Bill and Marta C. Bunge (1938-2022) in 2013 at the Memorial Conference for Aurelio Carboni, Milan.
Bill, George Janilidze, Francis Borceaux and others in 2013, during memorial conference for Aurelio Carboni, Milan
Massimo Galuzzi (1943-2023) and Stefano Kasangian with Bill in 2013 at University of Milan Mathematics Department, known as “Via Saldini”, during the memorial conference for Aurelio Carboni.
Bill in October 2013 at 50 years of FWL’s Funtorial Semantics of Algebraic Theories conference at Union College, Schenectady. Still from video by Michael Wright of the Archive Trust