note: from logic to geometry

• 30 August 2023
• math,
• note

How logic converted me to geometry.

Constructive Logic

• Finite semantics for fragments of intuitionistic logic, Felipe S. Albarelli and Rodolfo C. Ertola-Biraben

• Intuitionistic Logic Model Theory and Forcing, Melvin Fitting, 1969 . . . Again, emphasis on Frege’s project rather than topological approach to forcing

• John Bell, The development of categorical logic a historical look into categorical logic

• THE POINT OF POINTLESS TOPOLOGY, PETER JOHNSTONE, 1983 using locales (duals of frames — complete distributive lattices) to generalize topology to topos and thus to constructive math . . . not just topology for logicians

• Topology via Constructive Logic, Steven Vickers, 1996 . . . observe continuity through merely using reason as in programming computers

Topos and Homotopy

• Grothendieck’s Relative Point of View (Base Schemes), Hilado

• HoTT: Homotopy Type Theory

• CATEGORY THEORY IN CONTEXT, Emily Riehl, 2016 made available by Riehl

  • advanced but comprehensive pure category theory

• Categorification, John Baez, 1998

-Homotopy Cardinality via Extrapolation of Morava-Euler Characteristics, [Lior Yanovski](https://arxiv.org/search/math?searchtype=author&query=Yanovski%2C+L)

• NOTES ON TOPOSES AND LOCAL SET THEORIES, JOHN L. BELL, 1992: Revised 2020 made available by Bell. Approach Topos through logic rather than categories or topology

• “Sets in homotopy type theory”, Egbert Rijke & Bas Spitters marries topos with homotopy types.

• An Introduction to Category Theory: The Solutions, Harold Simmons, 18 September 2011

• Puzzling Through Exact Sequence, Ravi Vakil, 2021

• Intro Homotopy Types

• Intro String Diagrams

• Dependent Types at Work

• Algebraic Topology Prieview, Harvard Prof. Rastern

• Intro Topos, Baez

Grothendieck and Lawvere

Who else if not Yoneda and Kan?

• Who Is Alexander Grothendieck?, Winfried Scharlau

• Has the mathematical content of Grothendieck’s “Récoltes et Semailles” been used?

• Motives — Grothendieck’s Dream, Milne

• The Rising Sea: Grothendieck on simplicity and generality I, McLarty

• The Historical Developmentof Algebraic Geometry, J. Dieudonne

• F. W. Lawvere, Interview

• F. W. Lawvere, Subject Classification of Articles

• F. W. Lawvere, Collected works

Algebraic Geometry

• Bezout’s Theorem: A taste of algebraic geometry, Fitchett

• Self-study from “elementary algebra” to “algebraic geometry”, a historical route

• Why study algebraic geometry? Theorems, conjectures, resources

• Self-study from “differential” geometry & topology to algebraic geometry

• “Best” textbook(s) for algebraic geometry

• Intro texts on manifolds

• Texts for calculus on manifolds (before topology of manifolds)

• The Geometry of Schemes, Eisenbud & Harris

The Undergraduate Essentials

• Intro Algebra Notes, Prof. Paulin, UC Berkeley

• Intro Real Analysis Notes, Prof. Hunter, UC Davis

• Intro Topology Notes, Prof. Rognes, following Munkres

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