no code implementations • 25 Feb 2021 • Thierry Coquand, Henri Lombardi, Stefan Neuwirth
We provide a constructive treatment of basic results in the theory of central simple algebras.
Rings and Algebras Logic 16B70, 03F65, 19C30
no code implementations • 15 Dec 2020 • Marc Bezem, Thierry Coquand, Peter Dybjer, Martín Escardó
We give a new syntax independent definition of the notion of a generalized algebraic theory as an initial object in a category of categories with families (cwfs) with extra structure.
Category Theory Logic in Computer Science Logic 03G30 F.4.1
1 code implementation • 17 Jan 2017 • Thierry Coquand, Henri Lombardi, Stefan Neuwirth
its law, we call them equivariant systems of ideals for G: they describe all morphisms from G to meet-semilattice-ordered monoids generated by (the image of) G. Taking an article by Lorenzen (1953) as a starting point, we also describe all morphisms from a commutative ordered group G to lattice-ordered groups generated by G through unbounded entailment relations that preserve its order, are equivariant, and satisfy a regularity property invented by Lorenzen (1950); we call them regular entailment relations.
Logic Commutative Algebra Group Theory Primary 06F20, Secondary 06F05, 13A15, 13B22
4 code implementations • 7 Nov 2016 • Cyril Cohen, Thierry Coquand, Simon Huber, Anders Mörtberg
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.)
Logic in Computer Science Logic F.3.2; F.4.1
