Bill Lawvere obtained his Ph.D at Columbia university in 1963 with Samuel Eilenberg, (who was
the co-founder of Category Theory with S. MacLane in 1942–1945). He visited for a year at
Berkeley University, and after his PhD, during 1964–1967, he worked at the Forschungsinstitut f’ur
Mathematik at the famous ETH in Zurich; he began work on the Category of Categories (which is
defined as a meta-category or super-category), and was there directly influenced by Pierre
Gabriel’s seminars at Oberwolfach on Alexander Grothendieck’s Foundation of algebraic
Geometry.
Subsequently, he worked at The University of Chicago, Illinois, with Saunders Mac Lane
especially on Categorical Logics, using adjoint functors, algebraic semantics and universal
quantifiers (see ETAC and ETAS). During this time he also worked on Categorical
Dynamics.
He then moved to Dalhousie University in 1969, where in 1995 there was a celebration of 50 years
of Category Theory with Professor Saunders Mac Lane also being present. (Currently, there is also
an over-due celebration of 40 years of Categorical Dynamics, with Lawvere as one of the
founders).
He strongly opposed in 1970 the use of the War Measures Act on moral principles.
Since 1974, until his retirement in 2000, he was a Professor of Mathematics at University at
Buffalo, NY, often collaborating with Stephen Schanuel. He beacame an Emeritus Professor of
Mathematics and Adjunct, Emeritus Professor of Philosophy at the University at Buffalo,
NY.
[1] W.F. Lawvere. 1986. Categories in Continuum Physics, (Buffalo, N.Y. 1982), edited
by Lawvere and Stephen H. Schanuel (with Introduction by Lawvere pp 1-16), Springer
Lecture Notes in Mathematics No. 1174. (ISBN 3 − 540 − 16096 − 5).
[2] Lawvere, F. W., 1964, “An Elementary Theory of the Category of Sets”, Proceedings
of the National Academy of Sciences U.S.A., 52, 1506–1511.
[3] Lawvere, F. W., 1965, “Algebraic Theories, Algebraic Categories, and Algebraic
Functors”, Theory of Models, Amsterdam: North Holland, 413–418.
[4] Lawvere, F. W., 1966, “The Category of Categories as a Foundation for
Mathematics”, Proceedings of the Conference on Categorical Algebra, La Jolla, New
York: Springer-Verlag, 1–21.
[5] Lawvere, F. W., 1969a, “Diagonal Arguments and Cartesian Closed Categories”,
Category Theory, Homology Theory, and their Applications: II, Berlin: Springer,
134–145.
[6] Lawvere, F. W., 1969b, “Adjointness in Foundations”, Dialectica, 23, 281–295.
[7] Lawvere, F. W., 1970, “Equality in Hyper doctrines and Comprehension Schema as
an Adjoint Functor”, Applications of Categorical Algebra, Providence: AMS, 1-14.
[8] Lawvere, F. W., 1971, “Quantifiers and Sheaves”, Actes du Congrès International
des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
[9] Lawvere, F. W., 1972, “Introduction”, Toposes, Algebraic Geometry and Logic,
Lecture Notes in Mathematics, 274, Springer-Verlag, 1–12.
[10] Lawvere, F. W., 1975, “Continuously Variable Sets: Algebraic Geometry =
Geometric Logic”, Proceedings of the Logic Colloquium Bristol 1973, Amsterdam: North
Holland, 135–153.
[11] Lawvere, F. W., 1976, “Variable Quantities and Variable Structures in Topoi.”,
Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
[12] Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First Introduction
to Categories, Cambridge: Cambridge University Press.
[13] Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics.,
in Proc. Conf. Categorical Algebra- La Jolla., Eilenberg, S. et al., eds. Springer–Verlag:
Berlin, Heidelberg and New York., pp. 1-20.
[14] Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad.
Sci. USA, Mathematics, 50: 869-872.
[15] Lawvere, F. W.: 1969, Closed Cartesian Categories., Lecture held as a guest of the
Romanian Academy of Sciences, Bucharest.
[16] Lawvere, F. W., 1992, “Categories of Space and of Quantity”, The Space of
Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14–30.
[17] Lawvere, F. W., 1994a, “Cohesive Toposes and Cantor’s lauter Ensein”, Philosophia
Mathematica, 2, 1, 5–15.
[18] Lawvere, F. W., 1994b, “Tools for the Advancement of Objective Logic: Closed
Categories and Toposes”, The Logical Foundations of Cognition, Vancouver Studies in
Cognitive Science, 4, Oxford: Oxford University Press, 43–56.
[19] Lawvere, H. W (ed.), 1995. Springer Lecture Notes in Mathematics 274,:13–42.
[20] Lawvere, F. W., 2000, “Comments on the Development of Topos Theory”,
Development of Mathematics 1950-2000, Basel: Birkh’auser, 715–734.
[21] Lawvere, F. W., 2002, “Categorical Algebra for Continuum Micro-Physics”, Journal
of Pure and Applied Algebra, 175, no. 1–3, 267–287.
[22] Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge:
Cambridge University Press.
[23] Lawvere, F. W., 2003, “Foundations and Applications: Axiomatization and
Education. New Programs and Open Problems in the Foundation of Mathematics.”,
Bullentin of Symbolic Logic, 9, 2, 213–224.
[24] Lawvere, F.W., 1963, “Functorial Semantics of Algebraic Theories”, Proceedings of
the National Academy of Sciences U.S.A., 50, 869–872.
