mathematics

Peter J. Freyd

Peter J. Freyd is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Peter J. Freyd rather than just read about it. In short: Peter John Freyd (; born February 5, 1936) is an American mathematician, a professor at the University of Pennsylvania, known for work in category theory and for founding the False Memory Syndrome Foundation. Mathematics Freyd obtained his Ph.D. from Princeton University in 1960; his dissertation, on Functor Theory, was written under the supervision of Norman Steenrod and David Buchsbaum.

Key takeaways

Peter J. Freyd belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Peter J. Freyd to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Peter J. Freyd from memory before moving on to harder problems.

Reference excerpt

Mathematics Freyd obtained his Ph.D. from Princeton University in 1960; his dissertation, on Functor Theory, was written under the supervision of Norman Steenrod and David Buchsbaum. Freyd is best known for his adjoint functor theorem. He was the author of the foundational book Abelian Categories: An Introduction to the Theory of Functors (1964). This work culminates in a proof of the Freyd–Mitchell embedding theorem. In addition, Freyd's name is associated with the HOMFLYPT polynomial of knot theory, and he and Andre Scedrov originated the concept of (mathematical) allegories. In 2012, he became a fellow of the American Mathematical Society.

Publications Peter Freyd (1964). Abelian Categories: An Introduction to the Theory of Functors. Harper and Row. Reprinted with a forward as "Abelian Categories". Reprints in Theory and Applications of Categories. 3: 23–164. 2003. Peter J. Freyd and Andre Scedrov: Categories, Allegories. North-Holland (1999). ISBN 0-444-70368-3. Freyd Peter J (1999). "Path Integrals, Bayesian Vision, and Is Gaussian Quadrature Really Good?". Electron. Notes Theor. Comput. Sci. 29: 79. doi:10.1016/S1571-0661(05)80308-1. Freyd Peter J.; O'Hearn Peter W.; Power A. John; Takeyama Makoto; Street R.; Tennent Robert D. (1999). "Bireflectivity". Theor. Comput. Sci. 228 (1–2): 49–76. doi:10.1016/S0304-3975(98)00354-5.

References

External links Peter J. Freyd at the Mathematics Genealogy Project Printable versions of Abelian categories, an introduction to the theory of functors.

Illustrations

Worked examples

Example 1 — a first encounter with Peter J. Freyd

Start with the simplest possible case. Write down what Peter J. Freyd claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Peter J. Freyd before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Peter J. Freyd ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Peter J. Freyd

In research: Peter J. Freyd appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Peter J. Freyd in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Peter J. Freyd is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter J. Freyd outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Peter J. Freyd in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Peter J. Freyd means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Peter J. Freyd out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter J. Freyd in simple terms?

Peter John Freyd (; born February 5, 1936) is an American mathematician, a professor at the University of Pennsylvania, known for work in category theory and for founding the False Memory Syndrome Foundation. Mathematics Freyd obtained his Ph.D. from Princeton University in 1960; his dissertation…

Why does Peter J. Freyd matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Peter J. Freyd?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Peter J. Freyd.