Live briefing
Everything about Topos
Type of category in mathematics
In mathematics, a Grothendieck topos is a category that behaves like the category of sheaves of sets on a topological space. Topoi behave much like the category of sets and possess a notion of localization. Grothendieck topoi find applications in algebraic geometry. They are generalized by elementary topoi, which are used in logic. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ToposA 5-minute orientation
- Skim a recent paper: A neglected topos in behavioural normative economics: the opportunity and process aspect of freedomInfluential work since 2022
- Pick up a classic book: MoletownThe most-reprinted book on the subject
- Read the landmark paper: TOPOS3.2: a new version of the program package for multipurpose crystal-chemical analysisCited 973 times
- Go sideways: Grothendieck topologyA closely related topic
- Go sideways: Subobject classifierA closely related topic
📖 Definitions
Noun A literary theme or motif; a rhetorical convention or formula.
Noun A category that behaves like the category of sheaves of sets on a topological space (or, more generally, on a site).
Noun A toilet.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
TOPOS3.2: a new version of the program package for multipurpose crystal-chemical analysis
Nanocluster analysis of intermetallic structures with the program package TOPOS
TOPoS
TOPOS – A new constructive algorithm for nesting problems
Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalized Valuations
Homotopical algebraic geometry I: topos theory
O que são campos rupestres e campos de altitude nos topos de montanha do leste do Brasil?
Utopia with no Topos
🆕 Influential since 2022
📚 Books worth reading
MoletownTorben Kuhlmann · 2015- 📕Alexandro JodorowskyMichel Larouche · 1985
- 📕Carrière des Awirs & Carrière de l'Abbaye de FlôneG. Van den Broeck · 2004
The Traveller's Pathos – A Clinical Exercise in Byzantine PerspectiveDimitris Agouridas · 2019- 📕Los Rancheritos del Topo Chico de Catarino Leos RodríguezLuis Antonio Garza Torres · 2013
- 📕Il " topos" della lingua nella filosofia di PlatoneAntonio Francioni · 1991
El Viejo Topo treinta años despuésJordi Mir García · 2006- 📕Un manifesto topistaE Il Topo (Group of artists) · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Grothendieck topology In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category 𝒞 that makes the objects of 𝒞 act like the open sets…
- Subobject classifier In the mathematical field of category theory, a subobject classifier is a special object Ω {\displaystyle \Omega } of a category such that, informally…
- Stack (mathematics) In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of…
- Category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the…
- Fibred category Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the…
- Sheaf (mathematics) Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian…
- History of topos theory This article gives some very general background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being…
- Direct image functor In mathematics, the direct image functor describes how structured data assigned to one space can be systematically transferred to another space using a…