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Let P be the projection morphism of TM on S ( T M ) with respect to the first decomposition of (2.4).
Let ∇̃ be the Levi-Civita connection of M̃ and P be the projection morphism of (Gamma(TM)) to (Gamma(S TM))).
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(Cameron Davis is the projection designer).
commutes, where q is the quotient morphism.
commutes, where q is the quotient morphism of algebras.
The functor (o(i _!) then sends a collection (langle rho _cdot rangle ) to (rho (i)), and the morphism (alpha (f,o(i))) is the morphism (rho (f)).
We let be the set of all such morphisms.
We let (M X,Y) ) be the set of all such morphisms.
What matters are the morphisms between categories, given by functors.
Here, the right hand side is the complex of morphisms from ((B M ) q, b M | (B M ) q ) to (N, μ N 1 ).
We take L to be the category of labelled sets with morphisms that are injective maps respecting the labelling.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com