nLab: Adjoint Functor
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Community-maintained research wiki entry on adjunctions, giving the hom-set, unit-counit and universal-arrow definitions with many examples and properties. Useful for checking precise statements and finding references once the basic definition is familiar from a textbook.
More resources on Adjoint Functors
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
The Catsters: Adjunctions
Short chalkboard lecture series by Eugenia Cheng and Simon Willerton. It defines adjunctions through unit, counit and the triangle identities and shows equivalence with the hom-set definition. Follow-on videos cover adjunctions, monads and universal arrows.
What is an Adjunction? (Parts 1–3)
Three-part blog series that builds intuition for adjunctions from the free-forgetful pair between sets and vector spaces. Later parts present the hom-set definition and the unit and counit definition and show they are equivalent. The best free bridge between seeing the definition and understanding why it is natural, for learners who find the textbooks too dense.
nLab
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.