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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 26th 2017
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   Author: Urs
   Format: MarkdownItexThe term "flow of a vector field" used to redirect to _[[exponential map]]_, which however is really concerned with a somewhat different concept. So I have created now a separate entry _[[flow of a vector field]]_.

   The term “flow of a vector field” used to redirect to exponential map, which however is really concerned with a somewhat different concept. So I have created now a separate entry flow of a vector field.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 26th 2017
   • (edited Jun 26th 2017)
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   Author: David_Corfield
   Format: MarkdownItexWe have some SDG constructions [elsewhere](https://ncatlab.org/nlab/show/synthetic+differential+geometry#Constructions). Worth including here? Something like >A tangent vector field is a section of the map of $X^D \to X$ corresponding to evaluation at 0, so is a map $f: X \to X^D$, such that $f(x)(0) = x$. Uncurrying, this is equivalent to a map $f^{\ast}:X \times D \to X$, with $f^{\ast} (x, 0) = x$. Currying the first variable yields a map $D \to X^X$, i.e., to the group of diffeomorphisms of $X$.

   We have some SDG constructions elsewhere. Worth including here? Something like

   A tangent vector field is a section of the map of $X^D \to X$ corresponding to evaluation at 0, so is a map $f: X \to X^D$, such that $f(x)(0) = x$. Uncurrying, this is equivalent to a map $f^{\ast}:X \times D \to X$, with $f^{\ast} (x, 0) = x$. Currying the first variable yields a map $D \to X^X$, i.e., to the group of diffeomorphisms of $X$.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 26th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I wrote something [here](https://ncatlab.org/nlab/show/flow+of+a+vector+field#SyntheticDefinition). Unfortunately I don't really have the leisure for this at the moment

   Okay, I wrote something here. Unfortunately I don’t really have the leisure for this at the moment

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 26th 2017
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   Author: David_Corfield
   Format: MarkdownItexGreat, thanks. I linked to it from [[synthetic differential geometry]].

   Great, thanks. I linked to it from synthetic differential geometry.