We present and explore deep narrow- and medium-band data obtained with the Subaru and the Isaac Newton telescopes in the \sim 2 deg ^ { 2 } COSMOS field . We use these data as an extremely wide , low-resolution ( R \sim 20 - 80 ) IFU survey to slice through the COSMOS field and obtain a large sample of \sim 4000 Ly \alpha emitters ( LAEs ) from z \sim 2 to z \sim 6 in 16 redshift slices ( SC4K ) . We present new Ly \alpha luminosity functions ( LFs ) covering a co-moving volume of \sim 10 ^ { 8 } Mpc ^ { 3 } . SC4K extensively complements ultra-deep surveys , jointly covering over 4 dex in Ly \alpha luminosity and revealing a global ( 2.5 < z < 6 ) synergy LF with \alpha = -1.93 ^ { +0.12 } _ { -0.12 } , \log _ { 10 } \Phi ^ { * } _ { Ly \alpha } = { -3.45 ^ { +0.22 } _ { -0.29 } } Mpc ^ { -3 } and \log _ { 10 } L ^ { * } _ { Ly \alpha } = { 42.93 ^ { +0.15 } _ { -0.11 } } erg s ^ { -1 } . The Schechter component of the Ly \alpha LF reveals a factor \sim 5 rise in L ^ { * } _ { Ly \alpha } and a \sim 7 \times decline in \Phi ^ { * } _ { Ly \alpha } from z \sim 2 to z \sim 6 . The data reveal an extra power-law ( or Schechter ) component above L _ { Ly \alpha } \approx 10 ^ { 43.3 } erg s ^ { -1 } at z \sim 2.2 - 3.5 and we show that it is partially driven by X-ray and radio AGN , as their Ly \alpha LF resembles the excess . The power-law component vanishes and/or is below our detection limits above z > 3.5 , likely linked with the evolution of the AGN population . The Ly \alpha luminosity density rises by a factor \sim 2 from z \sim 2 to z \sim 3 but is then found to be roughly constant ( 1.1 ^ { +0.2 } _ { -0.2 } \times 10 ^ { 40 } erg s ^ { -1 } Mpc ^ { -3 } ) to z \sim 6 , despite the \sim 0.7 dex drop in UV luminosity density . The Ly \alpha /UV luminosity density ratio rises from 4 \pm 1 % to 30 \pm 6 % from z \sim 2.2 to z \sim 6 . Our results imply a rise of a factor of \approx 2 in the global ionisation efficiency ( \xi _ { ion } ) and a factor \approx 4 \pm 1 in the Ly \alpha escape fraction from z \sim 2 to z \sim 6 , hinting for evolution in both the typical burstiness/stellar populations and even more so in the typical ISM conditions allowing Ly \alpha photons to escape .