This paper discusses (1+1)d gapless phases with non-invertible global symmetries, including gapless SPT (gSPT) and gapless SSB (gSSB) phases. These phases are classified using the Symmetry Topological Field Theory (SymTFT), where each phase corresponds to a condensable algebra in the Drinfeld center of the symmetry category. The paper introduces a Hasse diagram, which partially orders these phases and defines a hierarchy of possible deformations. It identifies intrinsically gapless SPT (igSPT) and intrinsically gapless SSB (igSSB) phases, which cannot be deformed into gapped SPT or SSB phases. The paper also discusses the classification of gSPT and gSSB phases using functors between fusion categories and multi-fusion categories, respectively. It provides examples of these phases for specific symmetry groups and fusion categories, including $ Z_2 \times Z_2 $, $ \text{Rep}(D_8) $, and $ \text{Rep}(S_3) $. The paper also discusses the gauging of trivially acting non-invertible symmetries and the associated decomposition patterns. The analysis is based on the mathematical structure of the SymTFT and the properties of condensable algebras in the Drinfeld center. The paper concludes with a discussion of the physical implications of these phases, including the distinction between symmetry protected criticality and spontaneous symmetry breaking.This paper discusses (1+1)d gapless phases with non-invertible global symmetries, including gapless SPT (gSPT) and gapless SSB (gSSB) phases. These phases are classified using the Symmetry Topological Field Theory (SymTFT), where each phase corresponds to a condensable algebra in the Drinfeld center of the symmetry category. The paper introduces a Hasse diagram, which partially orders these phases and defines a hierarchy of possible deformations. It identifies intrinsically gapless SPT (igSPT) and intrinsically gapless SSB (igSSB) phases, which cannot be deformed into gapped SPT or SSB phases. The paper also discusses the classification of gSPT and gSSB phases using functors between fusion categories and multi-fusion categories, respectively. It provides examples of these phases for specific symmetry groups and fusion categories, including $ Z_2 \times Z_2 $, $ \text{Rep}(D_8) $, and $ \text{Rep}(S_3) $. The paper also discusses the gauging of trivially acting non-invertible symmetries and the associated decomposition patterns. The analysis is based on the mathematical structure of the SymTFT and the properties of condensable algebras in the Drinfeld center. The paper concludes with a discussion of the physical implications of these phases, including the distinction between symmetry protected criticality and spontaneous symmetry breaking.