Live briefing
Everything about Multicategory
Generalization of the concept of category that allows morphisms of multiple arity
In mathematics, a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of several variables. Multicategories are also sometimes called operads, or colored operads. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: MulticategoryA 5-minute orientation
- Skim a recent paper: Multicategory damage detection and safety assessment of post‐earthquake reinforced concrete structures using deep learningInfluential work since 2022
- Pick up a classic book: Homotopy Theory of Enriched Mackey FunctorsThe most-reprinted book on the subject
- Read the landmark paper: A comprehensive evaluation of multicategory classification methods for microarray gene expression cancer diagnosisCited 655 times
- Go sideways: Glossary of category theoryA closely related topic
- Go sideways: OperadA closely related topic
📖 Definitions
Noun A generalization of the concept of category that allows morphisms of multiple arity.
Adjective Of or relating to more than one category.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A comprehensive evaluation of multicategory classification methods for microarray gene expression cancer diagnosis
Multicategory Support Vector Machines
The “Shopping Basket”: A Model for Multicategory Purchase Incidence Decisions
Classification of multiple cancer types by multicategory support vector machines using gene expression data
Multicategory Proximal Support Vector Machine Classifiers
Multicategory Classification by Support Vector Machines
Application of genetic programming for multicategory pattern classification
A comprehensive evaluation of multicategory classification methods for microbiomic data
🆕 Influential since 2022
Multicategory damage detection and safety assessment of post‐earthquake reinforced concrete structures using deep learning
NWPU-MOC: A Benchmark for Fine-Grained Multicategory Object Counting in Aerial Images
Use and reporting of inverse-probability-of-treatment weighting for multicategory treatments in medical research: a systematic review
A High-Quality Multicategory SAR Images Generation Method With Multiconstraint GAN for ATR
Multimetric feature selection for analyzing multicategory outcomes of colorectal cancer: random forest and multinomial logistic regression models
📚 Books worth reading
- 📕Homotopy Theory of Enriched Mackey FunctorsNiles Johnson, Donald Yau · 2025
- 📕Identifying and Minimizing Measurement Invariance among Intersectional GroupsRachel A. Gordon, Tianxiu Wang · 2023
- 📕Weighting multicategory data to fit the common factor modelTomoichi Ishizuka · 1976
- 📕Testing dependence among serially correlated multi-category variablesPesaran, M. Hashem · 2006
- 📕An investigation of multicategory data factor analysis (MCDFA)Michel Henri Trahan · 1974
- 📕The nature and impact of multi-category prisoner populationsDavid Shewan · 1999
Introduction to artificial neural systemsJacek M. Zurada · 1992
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Glossary of category theory This is a glossary of properties and concepts in category theory in mathematics, including those in topos theory. (See also Outline of category theory…
- Operad In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output…
- Mac Lane's coherence theorem In category theory in mathematics, Mac Lane's coherence theorem, after Saunders Mac Lane, states that in any monoidal category, every well-formed diagram…
- Coproduct In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces…
- Product (category theory) In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas…
- PROP (category theory) In category theory, a branch of mathematics, a PROP is a symmetric strict monoidal category whose objects are the natural numbers n identified with the…
- F-algebra In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms…
- Algebraic stack In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli…