Category of fibre bundles

Let $𝖢$ be a subcategory of $𝖳 𝗈 𝗉$ and $𝑋$ be a space in $𝖢$ . The category of fibre bundles over $𝑋$ , denoted $𝖡 𝗎 𝗇 𝖽 𝖢 𝑋$ ,¹ is a category where an object is a fibre bundle and a morphism is a bundle map. #m/def/topology