mathematics

Heinrich Kleisli

Heinrich Kleisli 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 Heinrich Kleisli rather than just read about it. In short: Heinrich Kleisli (; October 19, 1930 – April 5, 2011) was a Swiss mathematician. He is the namesake of several constructions in category theory, including the Kleisli category and Kleisli triples.

Key takeaways

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

Reference excerpt

Heinrich Kleisli (; October 19, 1930 – April 5, 2011) was a Swiss mathematician. He is the namesake of several constructions in category theory, including the Kleisli category and Kleisli triples. He is also the namesake of the Kleisli Query System, a tool for integration of heterogeneous databases developed at the University of Pennsylvania. Kleisli earned his Ph.D. at ETH Zurich in 1960, having been supervised by Beno Eckmann and Ernst Specker. His dissertation was on homotopy and abelian categories. He served as an associate professor at the University of Ottawa before relocating to the University of Fribourg in 1966. He became a full professor at Fribourg in 1967.

Selected publications Kleisli, H., Every standard construction is induced by a pair of adjoint functors (Proc. Amer. Math. Soc. 16, AMS 544-546) (1965)

External links Heinrich Kleisli at the Mathematics Genealogy Project In memoriam: Prof. emerit. Heinrich Kleisli "Inside the AMS, Vol 58, No 8, Sept 2011" (PDF). (83k)

Illustrations

Worked examples

Example 1 — a first encounter with Heinrich Kleisli

Start with the simplest possible case. Write down what Heinrich Kleisli 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 Heinrich Kleisli 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 Heinrich Kleisli 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 Heinrich Kleisli

In research: Heinrich Kleisli 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 Heinrich Kleisli 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: Heinrich Kleisli is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 2011 deaths, Academic staff of the University of Fribourg, so understanding it makes those chapters shorter.
In everyday life: Look for Heinrich Kleisli 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 Heinrich Kleisli in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Heinrich Kleisli 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 Heinrich Kleisli out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Heinrich Kleisli in simple terms?

Heinrich Kleisli (; October 19, 1930 – April 5, 2011) was a Swiss mathematician. He is the namesake of several constructions in category theory, including the Kleisli category and Kleisli triples.

Why does Heinrich Kleisli 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 Heinrich Kleisli?

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 Heinrich Kleisli.