Geodesic
Soldered double linear morphisms
Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 68-78
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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 $Z_s((TT^*)_0\bold R^n)$.
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 $Z_s((TT^*)_0\bold R^n)$.
DOI : 10.21136/MB.1992.126230
Classification : 53C05, 55R05, 58A20
Keywords: tangent functor; natural transformations; fibrations; double vector space; double vector fibration; soldering 
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Vanžurová, Alena. Soldered double linear morphisms. Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 68-78. doi: 10.21136/MB.1992.126230

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