Definition 17.1.1 (Orthogonality). Let \(C\) be an \(\infty \)-category. A morphism \(l \colon A \to B\) is said to be left orthogonal to a morphism \(r \colon X \to Y\), written \(l \perp r\), if the following square is a pullback square:
Equivalently, for every solid commutative square
the anima of dashed fillers making both triangles commute is contractible. We then also say that \(r\) is right orthogonal to \(l\).
Given a collection of morphisms \(S\), we denote by \(S^\perp \) the collection of all morphisms that are right orthogonal to every morphism in \(S\), and by \({}^\perp S\) the collection of those that are left orthogonal to every morphism in \(S\).
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