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Full article: Simple Type Theory is not too Simple: Grothendieck’s ...
Apr 25, 2022 · Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of schemes in the simple type theory of the proof assistant Isabelle/HOL, and we discuss the …
Introduction and Motivation: The Outstanding Story of …
May 23, 2024 · Grothendieck himself called it “the fundamental theorem of the metric theory of tensor products”. It is likely that his work was rejected because he provided almost no proofs …
Alexander Grothendieck - Wikipedia
Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro (also known as Alexander Tanaroff), had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother, Johanna "Hanka" Grothendieck, came from a Protestant German family in Hamburg and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's …
Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 8 mins
May 29, 2022 · Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of …
Grothendieck: A Short Guide to His Mathematical and ... - Springer
- Grothendieck’s retirement from the IHES in 1970 is due to a diversity of factors, not reducible to a single perspective: technical exhaustion (after 20 years of extremely hard work, a point underlined by Cartier and Serre), individual liberation [g1986 1.65], social conscience [g1986 1.159], academic turmoil after May 1968 [g1986 1.156], disappoint...
- Email: [email protected]
- Published: Feb 18, 2021
Grothendieck fibration in nLab
Jul 29, 2024 · A Grothendieck fibration (named after Alexander Grothendieck, also called a fibered category or just a fibration) is a functor p: E → B p \colon E\to B such that the fibers E b …
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[2104.09366] Simple Type Theory is not too Simple: …
Apr 19, 2021 · Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of …
Grothendieck: A Short Guide to His Mathematical and …
The étalé strategy (1) governs Grothendieck’s world, traversed in all directions by sheaves. The main problem, understanding the mixture space-number, is explored through universal sheaf …
(PDF) Simple Type Theory is not too Simple: …
Apr 19, 2021 · This experiment shows that the simple type theory implemented in Isabelle can handle such elaborate constructions despite doubts raised about Isabelle's capability in that direction.
[PDF] Simple Type Theory is not too Simple: Grothendieck’s …
Apr 19, 2021 · This article outlines a method to encode most of the terms of Lean's dependent type theory into the simple type theory of Isabelle/HOL, and illustrates the formalisation of a …
universe in nLab
Nov 15, 2023 · Grothendieck universes. A Grothendieck universe is a set U U such that the following properties hold for U U: if x ∈ a ∈ U x \in a \in U, then x ∈ U x \in U; if a, b ∈ U a, b …
We wish to prove the Grothendieck-Riemann-Roch theorem for non-singular quasi-projective varieties. This requires a great deal of preparatory theory: the construction of the Chow ring, a …
Grothendieck’s problem Homotopy type theory Synthetic 1-groupoids Category theory The homotopy hypothesis...the study of n-truncated homotopy types (of semisimplicial sets, or of …
Grothendieck universe - Wikipedia
In mathematics, a Grothendieck universe is a set U with the following properties: If x is an element of U and if y is an element of x , then y is also an element of U . ( U is a transitive set .)
A brief tour of Grothendieck-Teichmuller theory Daniel Miller September 2, 2014 Everything in this brief note is inspired by Grothendieck’s revolutionary letter [Gro97]. 1 Motivation from …
GROTHENDIËCK TYPE NORMS. FOR BILINEAR FORMS ON C*-ALGEBRAS. UFFE HAAGERUP and TAKASHIITOH. Communicated by Norberto Salinas. ABSTRACT. We …
Topos Theory in a Nutshell - Department of Mathematics
Topos theory arose from Grothendieck's work in geometry, Tierney's interest in topology and Lawvere's interest in the foundations of physics. The two subjects are typical in this regard. An …
The Mysterious Disappearance of a Revolutionary Mathematician
May 9, 2022 · Rivka Galchen writes about Alexander Grothendieck, who was revered for revealing connections between seemingly unrelated realms—and then dropped out of society.
algebraic geometry - How and why does Grothendieck's work …
Oct 10, 2015 · Grothendieck's greatest contribution was to invent just that generalization : étale cohomology, which was based on his grandiose anterior re-creation of the tools of algebraic …
Grothendieck universe in nLab
Sep 15, 2024 · As a solution to foundational problems of category theory the concept was apparently brought up by Grothendieck (cf. below, p.149) in the context of 1958 Bourbaki …
GROTHENDIECK-TYPE INEQUALITIES IN COMBINATORIAL OPTIMIZATION. SUBHASH KHOT AND ASSAF NAOR. Abstract. We survey connections of the Grothendieck inequality …
Journal of Operator Theory :: a mathematics journal
Journal of Operator Theory. Volume 34, Issue 2, Fall 1995 pp. 263-283. Grothendieck type norms for bilinear forms on C*-algebras Authors: Uffe Haagerup (1) and Takashi Itoh (2)
topos in nLab
Jul 29, 2024 · We also have the (historically earlier) notion of Grothendieck topos: a Grothendieck topos is a topos that is neither too small nor too large, in that it is: cocomplete (not too small), …
On Turán-type problems and the abstract chromatic number
3 days ago · Authors: Dániel Gerbner, Hilal Hama Karim, Gaurav Kucheriya. View a PDF of the paper titled On Tur\'an-type problems and the abstract chromatic number, by D\'aniel Gerbner …
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