Carbon catalyst, battery electrode, and battery

A carbon catalyst has a carbon structure with a crystallite size Lc falling within 0.90 nm or more and 1.20 nm or less calculated through use of a Bragg angle of a diffraction peak fbroad at a diffraction angle 2θ of 24.0°±4.0° obtained by separating a diffraction peak in the vicinity of a diffraction angle 2θ of 26° in an X-ray diffraction pattern obtained by powder X-ray diffraction using a CuKα ray, and a carbon dioxide desorption amount from 650° C. to 1,200° C. of 97 μmol/g or less, a total of a carbon monoxide desorption amount and a carbon dioxide desorption amount from 650° C. to 1,200° C. of 647 μmol/g or less, or a carbon monoxide desorption amount from 650° C. to 1,200° C. of 549 μmol/g or less in a temperature programmed desorption method including measuring a carbon dioxide desorption amount from 25° C. to 1,200° C.