Kit for coating a nail or false nail, and more particularly for making up a nail or false nail, comprising: - a first photo-crosslinkable composition comprising, in a physiologically acceptable medium, at least one photo-crosslinkable compound a) comprising at least two acrylate functions, wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, and at least one carboxylic acid function, - a second photo-crosslinkable composition comprising, in a physiologically acceptable medium: • at least one photo-crosslinkable compound b) comprising at least one (poiy)urethane poly acrylate compound wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably polyurethane di(meth)acrylate compound, more preferentially polyurethane dimethacrylate compound, the photo-crosslinkable compound(s) b) comprising a (poly)oxyalkylene unit, in particular comprising a (poly)oxyethylene unit, preferably comprising from 1 to 100 oxyalkylene units, preferably from 5 to 50 oxyalkylene units, and preferentially approximately 8 to 10 oxyalkylene units, preferably identical to that contained in the first composition, • at least one photo-crosslinkable compound c) comprising at least two carbamate units obtained by reaction with at least one diisocyanate of isophorone diisocyanate type, the compound(s) c) correspond(s) to formula (XIII) below: in which formula (XIII): - R 1, R 2, R 3 and R 4, which may be identical or different, represent a hydrogen atom or a C 1 -C 10 alkyl chain, preferably a hydrogen atom or a methyl group, - j is between 1 and 10, preferably equal to 2, - A represents a C 1 -C 10 alkyl group, or a polyurethane comprising from 2 to 20 carbamate units. • at least one acrylate monomer, wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably (meth)acrylate monomer, more preferentially tetrahydrofurfuryl methacrylate. - a first photo-crosslinkable composition comprising, in a physiologically acceptable medium, at least one photo-crosslinkable compound a) comprising at least two acrylate functions, wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, and at least one carboxylic acid function, - a second photo-crosslinkable composition comprising, in a physiologically acceptable medium: • at least one photo-crosslinkable compound b) comprising at least one (poiy)urethane poly acrylate compound wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably polyurethane di(meth)acrylate compound, more preferentially polyurethane dimethacrylate compound, the photo-crosslinkable compound(s) b) comprising a (poly)oxyalkylene unit, in particular comprising a (poly)oxyethylene unit, preferably comprising from 1 to 100 oxyalkylene units, preferably from 5 to 50 oxyalkylene units, and preferentially approximately 8 to 10 oxyalkylene units, preferably identical to that contained in the first composition, • at least one photo-crosslinkable compound c) comprising at least two carbamate units obtained by reaction with at least one diisocyanate of isophorone diisocyanate type, the compound(s) c) correspond(s) to formula (XIII) below: in which formula (XIII): - R 1, R 2, R 3 and R 4, which may be identical or different, represent a hydrogen atom or a C 1 -C 10 alkyl chain, preferably a hydrogen atom or a methyl group, - j is between 1 and 10, preferably equal to 2, - A represents a C 1 -C 10 alkyl group, or a polyurethane comprising from 2 to 20 carbamate units. • at least one acrylate monomer, wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably (meth)acrylate monomer, more preferentially tetrahydrofurfuryl methacrylate. • at least one photo-crosslinkable compound b) comprising at least one (poiy)urethane poly acrylate compound wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably polyurethane di(meth)acrylate compound, more preferentially polyurethane dimethacrylate compound, the photo-crosslinkable compound(s) b) comprising a (poly)oxyalkylene unit, in particular comprising a (poly)oxyethylene unit, preferably comprising from 1 to 100 oxyalkylene units, preferably from 5 to 50 oxyalkylene units, and preferentially approximately 8 to 10 oxyalkylene units, preferably identical to that contained in the first composition, • at least one photo-crosslinkable compound c) comprising at least two carbamate units obtained by reaction with at least one diisocyanate of isophorone diisocyanate type, the compound(s) c) correspond(s) to formula (XIII) below: in which formula (XIII): - R 1, R 2, R 3 and R 4, which may be identical or different, represent a hydrogen atom or a C 1 -C 10 alkyl chain, preferably a hydrogen atom or a methyl group, - j is between 1 and 10, preferably equal to 2, - A represents a C 1 -C 10 alkyl group, or a polyurethane comprising from 2 to 20 carbamate units. - R 1, R 2, R 3 and R 4, which may be identical or different, represent a hydrogen atom or a C 1 -C 10 alkyl chain, preferably a hydrogen atom or a methyl group, - j is between 1 and 10, preferably equal to 2, - A represents a C 1 -C 10 alkyl group, or a polyurethane comprising from 2 to 20 carbamate units. • at least one acrylate monomer, wherein ALK represents a C 1 -C 6, preferably C 1 -C 2, more preferably C 1, alkyl group, such as CH 3, preferably (meth)acrylate monomer, more preferentially tetrahydrofurfuryl methacrylate.