Use of a binder for a lithium cell, wherein the binder comprises a polymer having a monomer unit derived from acrylic acid, and 1 to 2 kinds of monomer units derived from the compound shown by the following general formula or general formula, as constituents, and cross-linked by a cross-linking agent selected from the compounds described by the following general formulae to and to, and the polymer described by the following general formula; wherein R 1 represents hydrogen atom or a methyl group, and provided that in the case where R 2 is hydrogen atom, R 1 represents a methyl group; R 2 represents hydrogen atom, an alkyl group having 1 to 20 carbon atoms; an alkyl group having 1 to 20 carbon atoms, which is substituted with fluorine atom, a hydroxyl group or a cyano group; an aryl group having 6 to 10 carbon atoms; an arylalkyl group having 7 to 13 carbon atoms; an alkoxyalkyl group having 2 to 9 carbon atoms; an alkoxyalkoxyalkyl group having 3 to 9 carbon atoms; an aryloxyalkyl group having 7 to 13 carbon atoms; a morpholinoalkyl group having 5 to 7 carbon atoms; a trialkylsilyl group having 3 to 9 carbon atoms; an alicyclic hydrocarbon group having 6 to 10 carbon atoms, which has oxygen or does not have oxygen; a dialkylaminoalkyl group having 3 to 9 carbon atoms; a hexahydrophthalimide-N-alkyl group having 9 to 15 carbon atoms; the group shown by the following general formula wherein R 3 represents an alkylene group having 1 to 6 carbon atoms, which has a hydroxyl group as a substituent or does not have a substituent; R 4 represents hydrogen atom, an alkyl group having 1 to 6 carbon atoms, or a phenyl group; "v" represents an integer of 2 to 20; or the group shown by the following general formula wherein R 5 to R 7 each independently represent an alkyl group having 1 to 3 carbon atoms; R 8 represents an alkylene group having 1 to 3 carbon atoms, wherein R 11 represents hydrogen atom or a methyl group; R 12 represents hydrogen atom, or alkyl group having 1 to 6 carbon atoms; R 13 represents hydrogen atom, an alkyl group having 1 to 6 carbon atoms; a dialkylaminoalkyl group having 3 to 9 carbon atoms; or a hydroxyalkyl group having 1 to 6 carbon atoms, wherein R 27 to R 33 each independently represent an alkylene group having 1 to 3 carbon atoms, wherein R 34 to R 37 each independently represent an alkylene group having 1 to 6 carbon atoms; 1 represents an integer of 1 to 6; m represents an integer of 0 to 6; v1 and v2 each independently represent an integer of 0 or 1, wherein R 38 to R 45 each independently represent a hydrogen atom, a vinyl group or a vinylketone group, and at least two or more thereof are a vinyl group or a vinylketone group, wherein R 46 to R 48 each independently represent an alkylene group having 1 to 6 carbon atoms, wherein ring Ar 1 represents benzene ring or naphthalene ring; R 51 represents an alkylene group having 1 to 6 carbon atoms; "q" represents an integer of 2 to 4, wherein ring Ar 2 and ring Ar 3 each independently represent benzene ring or naphthalene ring; R 52 represents an alkylene group having 1 to 6 carbon atoms, wherein "p" represents an integer of 0 to 6, wherein, R 53 represents an alkylene group having 1 to 6 carbon atoms, wherein R 54 represents an alkylene group having 1 to 6 carbon atoms, which has or does not have a substituent, an arylene group having 6 to 10 carbon atoms, which has or does not have a substituent, or the group shown by the following general formula [12-A] wherein R 55 represents an alkyl group having 1 to 6 carbon atoms; R 56 represents an alkylene group having 1 to 6 carbon atoms; ring Ar 5 represents benzene ring or naphthalene ring; "b" represents an integer of 0 to 4; or the group shown by the following general formula [12-B] wherein R 57 represents an alkylene group having 1 to 6 carbon atoms; R 55, R 56, ring Ar 5 and "b" are the same as described above, wherein R 58 s each independently represent an alkyl group having 1 to 6 carbon atoms, which has or does not have a substituent, an aryl group having 6 to 10 carbon atoms, which has or does not have a substituent, or the group shown by the following general formula [13-A] wherein R 59 represents an alkyl group having 1 to 6 carbon atoms; R 60 represents an alkylene group having 1 to 6 carbon atoms; ring Ar 6 represents benzene ring or naphthalene ring; "c" represents an integer of 0 to 5, wherein R 61 represents an alkylene group having 1 to 6 carbon atoms, which has or does not have a substituent; an arylene group having 1 to 6 carbon atoms, which has or does not have a substituent; or the group shown by the following general formula [14-A] or [14-B] wherein R 62 represents an alkyl group having 1 to 6 carbon atoms; R 63 represents an alkylene group having 1 to 6 carbon atoms; ring Ar 7 represents benzene ring or naphthalene ring; and "a" represents an integer of 0 to 4; or the group shown by the following general formula [14-C] wherein R 64 represents an alkylene group having 1 to 6 carbon atoms; R 62, R 63, ring Ar 7, and "a" are the same as described above, and "s" represents an integer of 10 to 10000.