nLab
discrete group

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Context

Cohesive ∞-Toposes

cohesive topos

cohesive (∞,1)-topos

cohesive homotopy type theory

Backround

Definition

Presentation over a site

Structures in a cohesive (∞,1)-topos

structures in a cohesive (∞,1)-topos

Structures with infinitesimal cohesion

infinitesimal cohesion

Models

Contents

Idea

A discrete group is a group object in discrete spaces.

Equivalently this is just an ordinary group – a set with a group structure. One says discrete group for emphasis in a context where by default one is speaking about topological groups or Lie groups or groups equipped with other structure. See discrete ∞-groupoid for more discussion.

Revised on January 14, 2011 08:11:37 by Urs Schreiber (82.113.99.18)
Edit | Back in time (3 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: group, discrete category, smooth infinity-groupoid, category algebra, module, subobject classifier, group algebra, topological group, AKSZ sigma-model, sigma-model, diffeological space, string field theory, Dijkgraaf-Witten theory, discrete object, group cohomology, smooth space, Nielsen-Schreier theorem, normal subgroup, orbit, orientation, supergravity, Poisson sigma-model, action functional, Chern-Simons theory, foliation, Euclidean-topological infinity-groupoid, target space, simplicial topological group, infinity-Chern-Simons theory - contents, characteristic class, Topological Quantum Field Theories from Compact Lie Groups, topological Yang-Mills theory, model structure on operads, Whitehead tower in an (infinity,1)-topos, cohesive infinity-toposes - contents, Cahiers topos, A-model, B-model, Diaconescu's theorem, Courant sigma-model, Ext, infinity-Lie group, ordinary differential cohomology, circle n-bundle with connection, parallel transport, Lie group cohomology, Chern-Simons element, BF-theory, super infinity-groupoid, cohesive (infinity,1)-topos, geometric realization of cohesive infinity-groupoids, progroup, cohesive topos, cohesive site, infinity-cohesive site, discrete group, Cohesive Toposes -- Combinatorial and Infinitesimal Cases, Yetter model, free operad, cohesive (infinity,1)-topos -- structure sheaves, cohesive, Chern-Simons gravity, smooth infinity-groupoid -- structures, Some Thoughts on the Future of Category Theory, cohesive (infinity,1)-topos -- structures, infinity-representation, super-groupoid, synthetic differential infinity-groupoid, discrete infinity-groupoid, T-Duality and Differential K-Theory, locally contractible topological infinity-groupoid, smooth super infinity-groupoid, cohesive (infinity,1)-topos -- infinitesimal cohesion, cohesive (infinity,1)-topos -- structures II, internal site, concrete smooth infinity-groupoid, (infinity,1)-vector bundle, sigma-model -- exposition of classical sigma-models, sigma-model -- exposition of higher gauge theories as sigma-models, formally smooth object, higher Klein geometry, higher geometric quantization, higher dimensional Chern-Simons theory, stabilizer group, contents of contents, cohesive homotopy type theory, 6d Chern-Simons theory, Characteristic forms and geometric invariants, Yang-Mills instanton Floer homology, outer automorphism infinity-group, center of an infinity-group, ABJM theory, infinity-action, shape modality, 1-dimensional Chern-Simons theory, p-adic integer, infinitesimal shape modality, higher electric background charge coupling, infinite-dimensional Chern-Simons theory, 3d Chern-Simons theory, separated geometric morphism, coreduced object, smooth groupoid, projective resolution, twisted smooth cohomology in string theory, order of a group, synthetic differential super infinity-groupoid, holomorphic Chern-Simons theory, lattice in a vector space, geometry of physics, augmentation ideal, infinitesimal flat modality, field (physics), prequantum field theory, reduced object, 7d Chern-Simons theory, reduction modality, differential homotopy type theory, 5d Chern-Simons theory, 2d Chern-Simons theory, geometric quantization of non-integral forms, hyperbolic manifold, electroweak field, 4d Chern-Simons theory, concretification, level (Chern-Simons theory), Chern-Simons invariant, extended geometric quantization of 2d Chern-Simons theory, higher Atiyah groupoid, G-set, 1d Dijkgraaf-Witten theory