Added a reference to the thesis of Joel Couchman

]]>https://youtu.be/SMBriA04EOw?feature=shared talks about the above two notions (as far as I understand) and calls one of them to be a morphism, the other as comorphism.

When I understand more and get some confidence, I will try to add it here. ]]>

The first question one would want to check is whether either definition reduces — in the case where the base ring is $C^\infty(X)$ — to the ordinary homomorphisms of Lie algebroids (under the equivalence between such LR-pairs and Lie algebroids over $X$)?

(That said, I have not had the leisure to look closely at the articles, and may not find the time.)

]]>As the notion of morphisms of Lie algebroids, I am expecting this notion to be not so straightforward.

I came across two notions of morphisms of Lie-Rinehart algebras

1) something to do with "pullback", by Madeliene Jotz Lean in the work https://www.uni-math.gwdg.de/mjotz/JotzLean18c.pdf This seem to be natural and reminds me the notion of morphism of ringed spaces where we pushforward the sheaf on X to sheaf on Y when talking about morphisms of ringed spaces (X,O_X)--->(Y,O_Y). In my opinion the word "pushforward" should be used in the paper instead of "pullback".

2) notion of morphism in Camille Laurent-Gengoux and Ruben Louis work https://hal.science/hal-03462506/document.

I am trying to see if these two are related. I do not think they are. ]]>

A sufficient condition for that to happen is that the annihilator A_L={a \in A : aX=0}

be trivial. See Lemma 2.2 in https://arxiv.org/abs/2002.05718

Thank you,

Francisco Kordon,

franciscokordon at uca.fr ]]>

At *Lie-Rinehart pair* in Revision 8 somebody added the words

CAUTION: Elsewhere in the literature, it is : a Lie algebra morphism from $\mathfrak{g} \to Der(A)$

I don’t understand what this addition is good for. That homomorphism is stated precisely this way just three lines above.

Therefore I am removing that addition now. But please let me know if I am missing something.

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