Search for "Homotopy theory" in article titles:

1. Homotopy theory: In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipline. (Branch of mathematics) [100%] 2025-04-19 [Homotopy theory]
2. Rational homotopy theory: The natural setting of algebraic topology is the homotopy category. Restricting attention to simply-connected homotopy types and mappings between them allows the algebraic operation of localization (cf. (Mathematics) [81%] 2023-09-25 [Algebraic topology]
3. Homotopy type theory: In mathematical logic and computer science, homotopy type theory (HoTT /hɒt/) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies. This includes ... (Type theory in logic and mathematics) [81%] 2023-11-27 [Foundations of mathematics] [Type theory]...
4. Simple homotopy theory: In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It was originated by Whitehead in his 1950 paper "Simple homotopy type". [81%] 2023-12-25 [Homotopy theory] [Equivalence (mathematics)]...
5. Stable homotopy theory: In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which ... (The study of spectra) [81%] 2023-05-16 [Homotopy theory]
6. Rational homotopy theory: In mathematics and specifically in topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored. It was founded by Dennis Sullivan (1977) and Daniel Quillen (1969 ... (Mathematical theory of topological spaces) [81%] 2023-11-19 [Homotopy theory]
7. Rational homotopy theory: In mathematics and specifically in topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored. It was founded by Dennis Sullivan (1977) and Daniel Quillen (1969 ... (Mathematical theory of topological spaces) [81%] 2023-09-20 [Homotopy theory]
8. Chromatic homotopy theory: In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups. In this picture ... (Branch of mathematics) [81%] 2024-09-22 [Homotopy theory] [Cohomology theories]...
9. Stable homotopy theory: In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which ... (The study of spectra) [81%] 2025-02-04 [Homotopy theory]
10. Weak equivalence (homotopy theory): In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized in the axiomatic definition of a model category. (Homotopy theory) [70%] 2024-04-10 [Homotopy theory] [Homological algebra]...