Soldered double linear morphisms

Alena Vanžurová

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 1, page 68-78
  • ISSN: 0862-7959

Abstract

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Our aim is to show a method of finding all natural transformations of a functor T T * into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps f : C 0 → C 0 commuting with T T * -soldered automorphisms of a double vector space C 0 = V * × V × V * are investigated. On the set Z s ( C 0 ) of such mappings, appropriate partial operations are introduced. The natural transformations T T * → T T * are bijectively related with the elements of Z s ( ( T T * ) 0 𝐑 n ) .

How to cite

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Vanžurová, Alena. "Soldered double linear morphisms." Mathematica Bohemica 117.1 (1992): 68-78. <http://eudml.org/doc/29384>.

@article{Vanžurová1992,
abstract = {Our aim is to show a method of finding all natural transformations of a functor $TT^*$ into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps $f:C_0\rightarrow C_0$ commuting with $TT^*$-soldered automorphisms of a double vector space $C_0=V^*\times V\times V^*$ are investigated. On the set $Z_s(C_0)$ of such mappings, appropriate partial operations are introduced. The natural transformations $TT^*\rightarrow TT^*$ are bijectively related with the elements of $Z_s((TT^*)_0\mathbf \{R\}^n)$.},
author = {Vanžurová, Alena},
journal = {Mathematica Bohemica},
keywords = {tangent functor; natural transformations; fibrations; double vector space; double vector fibration; soldering; tangent functor; natural transformations; fibrations},
language = {eng},
number = {1},
pages = {68-78},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Soldered double linear morphisms},
url = {http://eudml.org/doc/29384},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Vanžurová, Alena
TI - Soldered double linear morphisms
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 1
SP - 68
EP - 78
AB - Our aim is to show a method of finding all natural transformations of a functor $TT^*$ into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps $f:C_0\rightarrow C_0$ commuting with $TT^*$-soldered automorphisms of a double vector space $C_0=V^*\times V\times V^*$ are investigated. On the set $Z_s(C_0)$ of such mappings, appropriate partial operations are introduced. The natural transformations $TT^*\rightarrow TT^*$ are bijectively related with the elements of $Z_s((TT^*)_0\mathbf {R}^n)$.
LA - eng
KW - tangent functor; natural transformations; fibrations; double vector space; double vector fibration; soldering; tangent functor; natural transformations; fibrations
UR - http://eudml.org/doc/29384
ER -

References

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  1. I. Kolář, On jet prolongations of smooth categories, Bull. Acad. Polon. Sci., Math., astr. et phys. Vol. XXIV 10 (1976), 883-887. (1976) MR0436190
  2. I. Kolář, Z.Radzisewski, Natural transformations of second tangent and cotangent functors, Czech. Math. Journal 38 (113) (1988), 274-279, Praha. (1988) MR0946296
  3. J. Pradines, Représentation des jets non holonomes par des morphismes vectoriels doubles soudés, C.R.Acad. Sci Paris Sér. A 278 (1974), 1523-1527. (1974) Zbl0285.58002MR0388432
  4. A. Vanžurová, Double vector spaces, Acta Univ. Palac. Olom., Fac. Rer. Nat., Math. XXVI 88 (1987), 9-25. (1987) MR1033327
  5. A. Vanžurová, Double linear connections, AUPO (in press). 
  6. A. Vanžurová, Natural transformations of the second tangent functor and soldered morphisms, AUPO, to appear in 1992. (1992) MR1212610

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