| Summary: | Let <i>R</i> be a Krasner hyperring. In this paper, we prove a factorization theorem in the category of Krasner <i>R</i>-hypermodules with inclusion single-valued <i>R</i>-homomorphisms as its morphisms. Then, we prove various isomorphism theorems for a smaller category, i.e., the category of Krasner <i>R</i>-hypermodules with strong single-valued <i>R</i>-homomorphisms as its morphisms. In addition, we show that the latter category is balanced. Finally, we prove that for every strong single-valued <i>R</i>-homomorphism <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo lspace="0pt">:</mo> <mi>A</mi> <mo>→</mo> <mi>B</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>a</mi> <mo>∈</mo> <mi>A</mi> </mrow> </semantics> </math> </inline-formula>, we have <inline-formula> <math display="inline"> <semantics> <mrow> <mi>K</mi> <mi>e</mi> <mi>r</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>K</mi> <mi>e</mi> <mi>r</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> <mo>=</mo> <mo>{</mo> <mi>x</mi> <mo>∈</mo> <mi>A</mi> <mo>∣</mo> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>f</mi> <mo>(</mo> <mi>a</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics> </math> </inline-formula>.
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