  We show that a decorated knot concordance $\mathcal{C}$ from $K_0$ to $K_1$
induces an $\mathbb{F}[U]$-module homomorphism \[G_{\mathcal{C}}:
HFK^{-}(-S^3,K_0) \to HFK^{-}(-S^3,K_1)\] which preserves the Alexander and
absolute $\mathbb{Z}_2$-Maslov gradings. Our construction generalizes the
concordance maps induced on $\widehat{HFK}$ studied by Juh\'asz and Marengon,
but uses the description of $HFK^{-}$ as a direct limit of maps between sutured
Floer homology groups discovered by Etnyre, Vela-Vick, and Zarev.

Geometric Topology