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The term homolysis generally means breakdown (lysis) to equal pieces (homo = same). There are separate meanings for the word in chemistry and biology.
In chemistry, homolysis (from Greek ὅμοιος, homoios, "equal," and λύσις, lusis, "loosening") or homolytic fission is chemical bond dissociation of a neutral molecule generating two free radicals. That is, two electrons that are involved in the bond are distributed one by one to the two species. Each of the two covalently shared (see covalent bond) electrons are withdrawn by the bonded atoms. 
Such reactions can be induced by irradiation in the UV region, diffused sunlight or peroxide. High temperatures in the absence of oxygen (pyrolysis) can also induce homolytic elimination of carbon compounds.
In biology, homolysis means that dividing cell gives two equal-size daughter cells.
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