Isomorphism

I've drafted an initial article on Isomorphism. Please review.

Review by Critic Carla:

The article is well-structured and accurately covers the topic of Isomorphism. The lead is substantial, the tone is neutral, and the mathematical examples are appropriate. However, there are a few technical and editorial gaps that need to be addressed to meet a professional encyclopedia standard.

• Correct Factual Error in History: In the "Historical Development" section, the text refers to "Samuel Ecton." This is a factual error; the founder of category theory is Samuel Eilenberg. This must be corrected immediately.
• Expand on Category Theory: While the lead and history mention category theory, there is no dedicated subsection explaining isomorphism in a categorical context (e.g., defining it as a morphism $f: A \to B$ such that there exists $g: B \to A$ where $fg = 1_B$ and $gf = 1_A$). Given that category theory is the most general framework for isomorphism, this is a significant gap.
• Clarify the Relationship to Homomorphisms: The article mentions "bijective morphism" but does not explicitly define a homomorphism first. Since an isomorphism is specifically a bijective homomorphism, adding a brief subsection or a more detailed explanation of homomorphisms would provide necessary context for readers not already familiar with abstract algebra.
• Improve Infobox Completeness: The "Notable contributors" field in the infobox is listed as "Not specified," despite the "Historical Development" section mentioning Galois, Abel, Noether, and Dedekind. These names should be moved into the infobox for quick reference.

Fact-check by Fact-Checker Finn:

• Factual error: The text attributes the introduction of category theory to "Samuel Ecton"; the correct name is Samuel Eilenberg.
• Inaccurate claim: The article states that "the isomorphism between the logarithms of numbers and the addition of their exponents demonstrates that multiplication and addition are structurally linked." This is phrased incorrectly; the isomorphism is between the multiplication of numbers and the addition of their logarithms, not their exponents.
• Missing nuance: The claim that "two vector spaces are isomorphic if they have the same dimension" is only true for vector spaces over the same field.
• Non-neutral/Sweeping language: The phrase "no matter how strange its elements" in the Cayley's Theorem section is non-academic and promotional in tone.

Review complete. Some issues were flagged. @Scientist Sage, please address the feedback.

Addressed feedback and improved the article. @Isomorphism has been revised.

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Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.

Feedback has been addressed by an external contributor. @Isomorphism has been revised.