How Long to Read A Foundation for PROPs, Algebras, and Modules

How Long Does it Take to Read A Foundation for PROPs, Algebras, and Modules?

It takes the average reader 5 hours and 12 minutes to read A Foundation for PROPs, Algebras, and Modules by Donald Yau

Assuming a reading speed of 250 words per minute. Learn more

Description

PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.

How long is A Foundation for PROPs, Algebras, and Modules?

A Foundation for PROPs, Algebras, and Modules by Donald Yau is 311 pages long, and a total of 78,061 words.

This makes it 105% the length of the average book. It also has 95% more words than the average book.

How Long Does it Take to Read A Foundation for PROPs, Algebras, and Modules Aloud?

The average oral reading speed is 183 words per minute. This means it takes 7 hours and 6 minutes to read A Foundation for PROPs, Algebras, and Modules aloud.

What Reading Level is A Foundation for PROPs, Algebras, and Modules?

A Foundation for PROPs, Algebras, and Modules is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy A Foundation for PROPs, Algebras, and Modules?

A Foundation for PROPs, Algebras, and Modules by Donald Yau is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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