The Lawvere family is happy to highlight The Lawvere Archives Posthumous Publications!
Bill left us a number of unpublished papers, essays, talks, prepared notes, and other writings from almost all periods of his career, covering many topics. There are also transcripts and notes of talks prepared by others. We are attempting to faithfully reformat and publish these materials over the next coming year(s). We don’t know Bill’s thoughts on the merits or shortcomings of these works. He marked some as drafts and others are not finalized, while many others he revised several times.
We have just added four more titles, dated July 14, 2025
1962 The Category of Probabilistic Mappings, With Applications to Stochastic Processes, Statistics, and Pattern Recognition, Spring 1962. Featuring Bill’s Abstract and Author Commentary from 2020. Reformatted by T. Fritz.
1989 A Philosophical Guide to Mathematics Based on the Objective Dialectics of Category Theory. Lectures in Milan. Reformatted by F. Marmolejo,
1989 Category Theory and the Foundations of Mathematics
Lectures in Cambridge. Reformatted by F. Marmolejo,
2011 Classifying Toposes & Positive Logic
Essay reformatted by F. Marmolejo
We invite you to browse all the Posthumous Publications and we are happy to say that they are no longer “unpublished”!
(For more details and to view the PDFs: https://lawverearchives.com/
Matías Menni and Francisco Marmolejo, have been tireless and invaluable in this work, and we are pleased to also thank Tobias Fritz for his generous assistance and insight. We are happy and proud to be continuing on this work with the help of these and other scholars and friends.
Our current list, by date and title, and the date added to Posthumous Publications:
1962 Category of Probablistic Mappings July 14, 2025
1989 Sheaves Large and Small February 9, 2025.
1997 Toposes of Laws of Motion. December 30, 2024.
1998 Outline of Synthetic Differential Geometry. (Revised November 1998).
2000 Induction is Idempotent Recursion in a Bicategory January 23, 2025.
2005 Categories and Everyday Human Activities. January 7, 2025. in English Italian Spanish
2007 Toposes in Geometry and Analysis February 9, 2025.
2007 The Role of History in Toposes in Geometry and Analysis February 9, 2025.
2009 Open Problems in Topos Theory. December 30, 2024
2011 Cantor’s ‘Lauter Einsen’ in the light of Galois and Grothendieck. January 23, 2025
2011 Classifying Toposes & Positive Logic July 14, 2025
2015 Alexander Grothendieck & the Modern Conception of Space. January 10, 2025.
2018 Basic Dynamics via Category Theory. January 23, 2025