nLab

A reflective subcategory is a full subcategory such that objects and morphisms in have “reflections” and in . Every object in looks at its own reflection via a morphism and the reflection of an object is equipped with an isomorphism . A canonical example is the inclusion of the category of abelian groups into the category of groups, whose reflector is the operation of abelianization. A useful pro…

On KK-compactification of 11-dimensional supergravity on a squashed 7-sphere with G₂-holonomy (M-theory on G₂-manifolds): On Kaluza-Klein compactification in supergravity: Mike Duff, Bengt Nilsson, Christopher Pope, Kaluza-Klein supergravity, Physics Reports Volume 130, Issues 1–2, January 1986, Pages 1-142 (spire:229417, doi:10.1016/0370-1573(86)90163-8) Michael Duff, Bengt Nilsson, Christopher …

Michael Duff is professor of theoretical physics at Imperial College London. He made foundational contributions to string theory and M-theory. Autobiographical notes around encountering Chris Isham: See also: 478 (2022) 2259 [doi:10.1098/rspa.2022.0166] On KK-compactification of 11-dimensional supergravity on a squashed 7-sphere with G₂-holonomy (M-theory on G₂-manifolds): Moustafa A. Awada, Mike…

Bengt E. W. Nilsson On Kaluza-Klein compactification in supergravity: Mike Duff, Bengt Nilsson, Christopher Pope, Kaluza-Klein supergravity, Physics Reports Volume 130, Issues 1–2, January 1986, Pages 1-142 (spire:229417, doi:10.1016/0370-1573(86)90163-8) Michael Duff, Bengt Nilsson, Christopher Pope: Kaluza-Klein Supergravity 2025, in: Half a Century of Supergravity – Part II: Structure and Prop…

superalgebra and (synthetic ) supergeometry Supergeometry is the (higher) geometry over the base topos on superpoints modeled on the canonical line object in there. As ordinary differential geometry studies spaces – smooth manifolds – that locally look like vector spaces, supergeometry studies spaces – supermanifolds – that locally look like super vector spaces. As ordinary algebraic geometry stu…

Lars Brink (1943-2022) Hermann Nicolai: Lars Brink 1943–2022, CernCourier (1 Mar 2023): Bengt E. W. Nilsson, Björn Jonson: Lars Brink – November 12, 1943 - October 29, 2022 [arXiv:2403.03776] François Englert: Lars Brink (1943–2022), Int. J. Mod. Phys. A 39 36 (2024) 2447001 [doi:10.1142/S0217751X24470018] George Savvidy: Lars Brink Colleague, Friend and Collaborator [arXiv:2408.09374] Paolo Di V…

François Englert (1932–2026) On Freund-Rubin compactifications of D=11 supergravity: On Lars Brink:

A semifunctor is a homomorphism between semicategories, like a functor is a homomorphism between categories. A semifunctor from a semicategory to a semicategory is a map sending each object to an object and each morphism in to morphism in , such that If is a category, then need not preserve its identity morphisms, but the composition axiom does require that it send them to idempotents in . In Rel…

homotopy hypothesis-theorem delooping hypothesis-theorem stabilization hypothesis-theorem Opetopic type theory (Finster 12) is a higher dimensional directed homotopy type theory for omega-categories, i.e. of infinity-categories in the full sense of -categories. Specifically, it realizes the higher-dimensional horn-filler conditions in the definition of opetopic omega-categories due to Palm as inf…

Foliated categories (French: catégories feuilletées), or simply foliations (not to be confused with the notion of foliations in differential geometry), were introduced by Jean Bénabou in unpublished work dating back to 1984. They are a weaker structure than fibered categories, but still allow one to test for various standard properties of functors fibre-wise. A functor makes its domain category a…

topology (point-set topology, point-free topology) see also differential topology, algebraic topology, functional analysis and topological homotopy theory Basic concepts fiber space, space attachment Kolmogorov space, Hausdorff space, regular space, normal space sequentially compact, countably compact, locally compact, sigma-compact, paracompact, countably paracompact, strongly compact Examples B…

On the limited principle of omniscience: On the weak limited principle of omniscience:

On the limited principle of omniscience: On the weak limited principle of omniscience: See also:

nLab polynomial time Last revised on June 19, 2026 at 12:24:15. See the history of this page for a list of all contributions to it.

Andrée Charles Ehresmann (née Bastiani) is a category theorist. She is editor in chief of the journal Cahiers de Topologie et Géométrie Différentielle Catégoriques, founded by her late husband Charles Ehresmann. Andrée Ehresmann’s early papers were published under her maiden name Andrée Bastiani, and during a transition period under the hyphenated surname Bastiani-Ehresmann. On internalization of…

Predicting what came to be called the fractional quantum anomalous Hall effect in fractional Chern insulators: review: On higher order topological insulators (with protected corner-modes beyond the edge-modes): On topological crystalline insulators with focus on the Wilson lines of the Berry connection: On “delicate” unstable topological phases of matter: Aleksandra Nelson, Titus Neupert, Tomáš B…

∞-Lie theory (higher geometry) Background Smooth structure Higher groupoids Lie theory ∞-Lie groupoids ∞-Lie algebroids Formal Lie groupoids Cohomology Homotopy Related topics Examples -Lie groupoids -Lie groups -Lie algebroids -Lie algebras A Lie 2-algebra is to a Lie 2-group as a Lie algebra is to a Lie group. Thus, it is a vertical categorification of a Lie algebra. A (“semistrict”) Lie 2-alge…

On configuration spaces of points in algebraic topology: On the Morava E-theory of configuration spaces of points: On the ordinary cohomology of configuration spaces of points via spectral sequences:

indiscernible sequence? Morley sequence? Ramsey theorem? Erdos-Rado theorem? Ehrenfeucht-Fraïssé games (back-and-forth games) Hrushovski construction? generic predicate? Given a collection of finite(ly-generated) first-order structures which formally resemble collections of finite(ly-generated) substructures found inside an infinite structure, there are additional assumptions on such collections …