Mean scaling relations between the halo virial mass and a number of halo properties described in Sect. 3.1, at z = 0 evaluated in different cosmic-web types. Shown intrinsic properties are V_max (panel a), R_s (panel b) C_vir (panel c), λ_B (panel d), T/|U| (panel e), 𝒯_h (panel f), ℰ_h (panel g). Nonlocal properties: local Mach number ℳ₅ (panel h), Δ₅ (panel i), 𝒟₅ (panel j). Environmental properties: local dark matter density (panel k) and tidal anisotropy 𝒯_A (panel l). The error bars denote the error in the mean in each mass bin.