Fibre bundle
Bundle map
Let 𝐹 →𝐸 𝜋↠𝑋 and 𝐹′ →𝐸′ 𝜋′↠𝑋 be fibre bundles over a common base space 𝑋 in a category 𝖢.
A bundle map 𝑓 :𝐸 →𝐸′ is a map 𝑓 ∈𝖢(𝐸,𝐸′) such that

commutes in 𝖢.
Bundle maps are the morphisms of 𝖡𝗎𝗇𝖽𝖢𝑋.
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