Cathode, membrane electrode assembly, and battery

A cathode of a battery including an electrolyte membrane, the cathode comprising:

• a first layer which contains 0.3 mg/cm2 or more and 9.0 mg/cm2 or less of a carbon catalyst;
• and
• a second layer which is arranged between the electrolyte membrane and the first layer in the battery, and which contains 0.002 mg/cm2 or more and 0.190 mg/cm2 or less of platinum,
• wherein the carbon catalyst contains iron,
• wherein the carbon catalyst exhibits a weight reduction rate at 200° C. to 1,200° C. of 12.0 wt % or less measured by thermogravimetric analysis in a nitrogen atmosphere, and
• wherein the carbon catalyst has a carbon structure that exhibits, in X-ray absorption fine structure analysis of a K absorption edge of the iron, the following (a) and/or (b):
• (a) a ratio of a normalized absorbance at 7,130 eV to a normalized absorbance at 7,110 eV is 7.0 or more;
• and
• (b) a ratio of a normalized absorbance at 7,135 eV to a normalized absorbance at 7,110 eV is 7.0 or more.