Catalyst and electrode catalyst layer, membrane electrode assembly, and fuel cell using the catalyst

A catalyst comprising:

• a catalyst support;
• and
• a catalyst metal supported on the catalyst support,
• wherein a mode radius of pore distribution of pores having a radius of 1 nm or more of the catalyst is 1 nm or more and less than 5 nm,
• wherein the catalyst metal is supported inside the pores of which mode radius is 1 nm or more and less than 5 nm,
• wherein the mode radius is equal to or less than an average particle radius of the catalyst metal, and
• wherein a pore volume of the pores of which mode radius is 1 nm or more and less than 5 nm existing in the catalyst is 0.4 cc/g support or more.