# Kerodon

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Definition 3.4.2.1. A commutative diagram of simplicial sets

$\xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & A_0 \ar [d] \\ A_1 \ar [r] & A_{01} }$

is a homotopy pushout square if, for every Kan complex $X$, the diagram of Kan complexes

$\xymatrix@R =50pt@C=50pt{ \operatorname{Fun}(A_{01}, X) \ar [r] \ar [d] & \operatorname{Fun}(A_{0}, X) \ar [d] \\ \operatorname{Fun}(A_1, X) \ar [r] & \operatorname{Fun}(A, X) }$

is homotopy pullback square (Definition 3.4.1.1).