Category of quadratic Lie algebras

The category of quadratic Lie algebras $𝖰 𝖫 𝗂 𝖾 𝕂$ is a category where an object is a Quadratic Lie algebra over $𝕂$ and a morphism is a isometric Lie algebra homomorphism. #m/def/lie Thus if $𝑓 \in 𝖰 𝖫 𝗂 𝖾 𝕂 (𝔤, 𝔥)$ then

⟨ 𝑓 (𝑥), 𝑓 (𝑦) ⟩ 𝔥 = ⟨ 𝑥, 𝑦 ⟩ 𝔤

for any $𝑥, 𝑦 \in 𝔤$ .

#state/tidy | #lang/en | #SemBr