The *opposite category of a Category 𝒞 𝒞 \mathcal{C} is a category 𝒞 m a t h r m o p superscript 𝒞 𝑚 𝑎 𝑡 ℎ 𝑟 𝑚 𝑜 𝑝 \mathcal{C}^{mathrm{op}} where