Quotient category

Given a category $𝖢$ and a congruence relation on hom-sets $\equiv$ , the quotient category $𝖢 / \equiv$ has the same objects as $𝖢$ and congruence classes as morphisms, i.e.

𝖢 / \equiv (𝑋, 𝑌) = {[𝑓] : 𝑓 \in 𝖢 (𝑋, 𝑌)}

Examples

$𝖳 𝗈 𝗉 / ≃$ $= 𝖳 𝗈 𝗉 / ≃$ where $≃$ is Homotopy of continuous maps.

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