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Everything about Identity type
Notion of equality in type theory
In type theory, a branch of mathematics, the identity type represents the concept of equality. It is also known as propositional equality to differentiate it from "judgemental equality". Equality in type theory is a complex topic and has been the subject of research, such as the field of homotopy type theory. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Identity typeA 5-minute orientation
- Skim a recent paper: Fully-automated and ultra-fast cell-type identification using specific marker combinations from single-cell transcriptomic dataInfluential work since 2022
- Pick up a classic book: The Tragedy of Pudd'nhead WilsonThe most-reprinted book on the subject
- Read the landmark paper: A threat in the air: How stereotypes shape intellectual identity and performance.Cited 4,370 times
- Go sideways: Uniqueness of identity proofsA closely related topic
- Go sideways: Homotopy type theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A threat in the air: How stereotypes shape intellectual identity and performance.
A rellich type identity and applications
Alterations in Beta Cell Identity in Type 1 and Type 2 Diabetes
The identity type weak factorisation system
Cell-type identity of the avian cochlea
Cell-type identity of the avian utricle
Identity of Pyrenophora isolates causing net-type and spot-type lesions on barley
Generalization of Popoviciu-Type Inequalities Via Fink’s Identity
🆕 Influential since 2022
Fully-automated and ultra-fast cell-type identification using specific marker combinations from single-cell transcriptomic data
Single-cell eQTL mapping identifies cell type–specific genetic control of autoimmune disease
A single-cell Arabidopsis root atlas reveals developmental trajectories in wild-type and cell identity mutants
Identification of a broadly fibrogenic macrophage subset induced by type 3 inflammation
📚 Books worth reading
The Tragedy of Pudd'nhead WilsonMark Twain · 1758
DivergentVeronica Roth · 2010
Nesnesitelná lehkost bytíMilan Kundera · 1984
RootsAlex Haley · 1861
InsurgentVeronica Roth · 2011
AllegiantVeronica Roth · 2011
MiddlesexJeffrey Eugenides · 2002
Jacob have I lovedKatherine Paterson · 1980
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Uniqueness of identity proofs In type theory, uniqueness of identity proofs (UIP) is a possible axiom for dependent type theory which asserts that any two proofs of the same equality…
- Homotopy type theory In mathematical logic and computer science, homotopy type theory (HoTT) includes various lines of development of intuitionistic type theory, based on the…
- Intuitionistic type theory Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of…
- Type theory In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects by…
- Inductive type In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type.…
- Thomas Streicher Thomas Streicher (11 February 1958 – 2 January 2025) was an Austrian mathematician who was a Professor of Mathematics at Technische Universität Darmstadt…
- History of type theory The type theory was initially created to avoid paradoxes in a variety of formal logics and rewrite systems. Later, type theory referred to a class of formal…
- Setoid In mathematics, a setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional…