Theoretical equivalence
This page is devoted to the seemingly innocuous question: when are two logical or scientific theories equivalent?
Literature
Morita equivalence , arising from categorical logic
- Barrett & Halvorson, 2015: Morita equivalence (arxiv, pdf)
- Hans Halvorson gave this talk at Stanford’s 2017 CSLI workshop
- Slides from an older, similar talk
- Tsementzis, 2016: A syntactic characterization of Morita equivalence (arxiv, slides)
- Johnstone, 2002: Sketches of an Elephant, Sec D1.4: Syntactic categories
- Curious results about Morita equivalence of regular/coherent theories
Algebraic background: Module theory and Morita equivalence of rings
- Mac Lane & Birkhoff, 1999: Algebra, Ch. V, Modules
- Introduction to modules from the categorical viewpoint
- Really, any other algebra textbook would do just as well
- Adkins & Weintraub, 1999: Algebra, Sec 7.2: Multilinear algebra
- Introduction to bimodules and their homs and tensor products
- Lam, 1998: Lectures on Rings and Modules, Ch. 7: Matrix rings, categories of
modules, and Morita theory
- Textbook exposition of Morita theory for rings
- Basis for lecture notes by Rabib Islam with greater 2-categorical emphasis