Concept

Timeline of category theory and related mathematics

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: of abstract algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic and set theory in the categorical context such as algebraic set theory; Foundations of mathematics building on categories, for instance topos theory; Abstract geometry, including algebraic geometry, categorical noncommutative geometry, etc. Quantization related to category theory, in particular categorical quantization; Categorical physics relevant for mathematics. In this article, and in category theory in general, ∞ = ω.

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https://en.wikipedia.org/wiki/Timeline_of_category_theory_and_related_mathematics

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Related lectures (18)

Introduction to simplicial sets: Simplicial sets

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

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From (Model) Categories to Quasicategories

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This thesis makes two independent contributions at the interface of combinatorics and topology. Part I studies obstructions to Quillen model structures on categories equipped with intrinsic discrete homotopy theories. The central example is x-homotopy on graphs, which admits an explicit homotopy category but has resisted all attempts to produce a compatible model structure. We identify three distinct obstructions: the Campion--Goodwillie obstruction in cocomplete categories, where iterated wedge constructi

EPFL2026

Filter quotients and non-presentable (∞,1)-toposes

Nima Rasekh

We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -ca ...

2021

Order-adjoint monads and injective objects

Given a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T ...

Elsevier2010

Related people (1)

Kathryn Hess Bellwald

Kathryn Hess Bellwald received her PhD from MIT in 1989 and held positions at the universities of Stockholm, Nice, and Toronto before moving to the EPFL.Her research focuses on algebraic topology and its applications, primarily in the life sciences, but also in materials science. She has published extensively on topics in pure algebraic topology including homotopy theory, operad theory, and algebraic K-theory. On the applied side, she has elaborated methods based on topological data analysis for high-throughput screening of nanoporous crystalline materials, classification and synthesis of neuron morphologies, and classification of neuronal network dynamics. She has also developed and applied innovative topological approaches to network theory, leading to a powerful, parameter-free mathematical framework relating the activity of a neural network to its underlying structure, both locally and globally.In 2016 she was elected to Swiss Academy of Engineering Sciences and was named a fellow of the American Mathematical Society and a distinguished speaker of the European Mathematical Society in 2017. In 2021 she gave an invited Public Lecture at the European Congress of Mathematicians. She has won several teaching prizes at EPFL, including the Crédit Suisse teaching prize and the Polysphère d’Or.

Related units (2)

MATH - Divers

Laboratory for Topology and Neuroscience

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