Editing Tensor (section)

=== Geometric objects ===
The transformation law for a tensor behaves as a [[functor]] on the category of admissible coordinate systems, under general linear transformations (or, other transformations within some class, such as [[local diffeomorphism]]s).  This makes a tensor a special case of a geometrical object, in the technical sense that it is a function of the coordinate system transforming functorially under coordinate changes.<ref>{{cite journal |last1=Haantjes |first1=J. |author2-link=Gerard Laman |last2=Laman |first2=G.  |title=On the definition of geometric objects. I |journal=Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences |volume=56 |issue=3 |pages=208–215 |date=1953 }}</ref>  Examples of objects obeying more general kinds of transformation laws are [[jet (mathematics)|jets]] and, more generally still, [[natural bundle]]s.<ref>{{citation|first=Albert|last=Nijenhuis|author-link=Albert Nijenhuis|chapter-url=http://www.mathunion.org/ICM/ICM1958/Main/icm1958.0463.0469.ocr.pdf|chapter=Geometric aspects of formal differential operations on tensor fields|title=Proc. Internat. Congress Math.(Edinburgh, 1958)|year=1960|publisher=Cambridge University Press|pages=463–9|access-date=2017-10-26|archive-date=2017-10-27|archive-url=https://web.archive.org/web/20171027025011/http://www.mathunion.org/ICM/ICM1958/Main/icm1958.0463.0469.ocr.pdf|url-status=dead}}.</ref><ref>{{citation|url=https://projecteuclid.org/download/pdf_1/euclid.jdg/1214430830|title=On the theory of geometric objects|first=Sarah |last=Salviori|journal=[[Journal of Differential Geometry]]|year=1972|volume=7|issue=1–2|pages=257–278|doi=10.4310/jdg/1214430830|doi-access=free}}.</ref>