Curable water-based composition, active-energy-ray-curable water-based composition, active-energy-ray-curable water-based ink, stored container, two-dimensional or three-dimensional image forming apparatus, two-dimensional or three-dimensional image forming method, cured product, and decorated body

A hydrogel, comprising

• a reaction product of an acrylamide compound (A1) represented by General formula (A1) below with an acrylamide compound (B1) represented by General formula (B1) below or an acrylamide compound (A2) represented by General formula (A2-1) below or General formula (A2-2) below,
• where in the General formula (A1), X represents an alkylene group containing from 1 through 6 carbon atoms, and Y represents a group represented by General formula (A1a) below or General formula (A1b) below,
• where in the General formula (A1a), R1 represents an alkyl group containing from 1 through 10 carbon atoms, and * represents a bonding site with X,
• where in the General formula (A1b), R1 represents an alkyl group containing from 1 through 10 carbon atoms, and * represents a bonding site with X,
• where in the General formula (B1), R2 represents a hydrogen atom or an alkyl group containing from 1 through 4 carbon atoms and may have a branched structure, R3 represents a hydrogen atom or a methyl group, and Z represents an alkylene group containing from 1 through 30 carbon atoms or a group obtained by substituting oxygen, nitrogen, and sulfur atoms for some of the carbon atoms of the alkylene group containing from 1 through 30 carbon atoms and may contain a polar functional group, a (meth)acrylate group, or a (meth)acrylamide group as a substituent,
• where in the General formula (A2-1), R4 represents an alkyl group containing from 1 through 6 carbon atoms, X represents an alkylene group containing from 1 through 6 carbon atoms, and Y represents a group represented by General formula (A2a-1) below or General formula (A2b-1) below,
• where in the General formula (A2a-1), R5 represents an alkyl group containing form 1 through 10 carbon atoms, and * represents a bonding site with X,
• where in the General formula (A2b-1), R5 represents an alkyl group containing from 1 through 10 carbon atoms, and * represents a bonding site with X,
• where in the General formula (A2-2), a ring X1 represents a nitrogen atom-containing ring structure containing from 2 through 5 carbon atoms, R6 represents a single bond or an alkylene group containing from 1 through 3 carbon atoms, and R7 represents a straight-chained or branched alkyl group containing from 1 through 10 carbon atoms.