Universal Construction (nLab)
by nLab contributors · nLab
Wiki entry explaining how specifying the maps into or out of an object determines it up to isomorphism, with worked cases for products, free groups, tensor products, and initial and terminal objects, plus the Yoneda-lemma justification.
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Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.