I will post an answer that uses an advanced microbiology book, as they are careful to get their terms very accurate.
Glycolysis is part of both respiration and fermentation.
Microbiology: A Clinical Approach, Second Edition By Anthony Strelkauskas, Angela Edwards, Beatrix Fahnert, Greg Pryor, Jennifer Strelkauskas
(Side note- Non-introductory microbiology books don't count fermentation as part of respiration. As I discovered when looking into whether humans did anaerobic respiration, here Are humans capable of both anaerobic respiration, and lactic acid fermentation?Are humans capable of both anaerobic respiration, and lactic acid fermentation? And as is shown in the diagram above, from that advanced microbiology text. Biology 101 texts, and human biology texts, are more relaxed(arguably wrong), with their definition)