filtered category

nonempty category such that for any two objects 𝑥, 𝑦 there exists a diagram 𝑥→𝑧←𝑦 and for every two parallel arrows 𝑓,𝑔: 𝑥→𝑦 there exists an ℎ: 𝑦→𝑧 such that ℎ∘𝑓=ℎ∘𝑔