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

*2. Elementary Theory of the Category of Sets*, **Proceedings of the National Academy of Science 52**, No. 6 (December
1964), 1506-1511.

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

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

5. *The Category of
Categories as a Foundation for Mathematics*, **La Jolla Conference on Categorical Algebra**,
Springer-Verlag (1966), 1-20.

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.

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

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

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

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.

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

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

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

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

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.

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.

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

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.

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

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

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

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

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

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

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.

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

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).

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.

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.

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.

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.

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.

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.

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).

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).

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).

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.

39. *Categorie e
Spazio: Un Profilo,* ** Lettera
matematica PRISTEM 31**, Springer, Italy, (1999), 35-50. [Reprinted in

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

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.

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.

44. *Categorical
algebra for continuum microphysics*, **Journal of Pure and Applied algebra 175**,** **(2002),
267-287.

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.

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

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.*]

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

50. *Concetti fondazionali
espliciti nell'insegnamento della matematica , *

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).

51. *Left and Right
Adjoint Operations on Spaces and Data Types, For Dana Scott's Seventieth Birthday,
Copenhagen 2002*,

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.

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)

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].

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)

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).

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

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)

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*wlawvere@acsu.buffalo.edu*