The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
From Groups to Groupoids: a Brief Survey
Abstract
A groupoid should be thought of as a group with many objects, or with many identities. A precise definition is given below. A groupoid with one object is essentially just a group. So the notion of groupoid is an extension of that of groups. It gives an additional convenience, flexibility and range of applications, so that even for purely group-theoretical work, it can be useful to take a path through the world of groupoids.
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Cites
Whitehead, J. H. C. (1949) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1949-09175-9 · Cited by 815
Classifying spaces and spectral sequences
Segal, G. (1968) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684591 · Cited by 764
Complex Cobordism and Stable Homotopy Groups of Spheres
Ravenel, D. (2003) · American Mathematical Society eBooks · doi:10.1090/chel/347 · Cited by 720 · cited 1×
“The term is due to H. Miller, and the book [122] gives a good account of the uses in stable homotopy theory, also developed by Morava [108].”
BackgroundGeneral Theory of Natural Equivalences
Eilenberg, S., & MacLane, S. (1945) · Transactions of the American Mathematical Society · doi:10.2307/1990284 · Cited by 575
Van Kampen theorems for diagrams of spaces
Ronald Brown, A., & Loday, J.-L. (1987) · Topology · doi:10.1016/0040-9383(87)90004-8 · Cited by 400
Versal deformations and algebraic stacks
Artin, M. (1974) · Inventiones Mathematicae · doi:10.1007/bf01390174 · Cited by 339
Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes
Haefliger, A. (1958) · Commentarii Mathematici Helvetici · doi:10.1007/bf02564582 · Cited by 158
Noetherian Localisations of Categories of Cobordism Comodules
Morava, J. (1985) · Annals of Mathematics · doi:10.2307/1971192 · Cited by 125
Maps between classifying spaces
Dwyer, W. G., & Zabrodsky, A. (1987) · Lecture notes in mathematics · doi:10.1007/bfb0083003 · Cited by 111
Intersection theory on algebraic stacks and Q-varieties
Gillet, H. (1984) · Journal of Pure and Applied Algebra · doi:10.1016/0022-4049(84)90036-7 · Cited by 106
Cited by
Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
Stewart, I., Golubitsky, M., & Pivato, M. (2003) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/s1111111103419896 · Cited by 337
Higher-dimensional algebra and topological quantum field theory
Baez, J. C., & Dolan, J. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531236 · Cited by 317
Metadata
- Authors
- Brown, R.
- Venue
- Bulletin of the London Mathematical Society
- Publisher
- Wiley
- Published
- 1987-03
- Volume
- 19
- Issue
- 2
- Pages
- 113-134
- ISSN
- 0024-6093 (ISSN-L)
- OpenAlex
- W1995530003
- Cited by
- 324
- References
- 13
- FWCI
- 5.96
- Type
- journal article
- Language
- en
- Open access
- closed
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