How Long to Read Surface Diagrams for Gray-categories

How Long Does it Take to Read Surface Diagrams for Gray-categories?

It takes the average reader 2 hours and 13 minutes to read Surface Diagrams for Gray-categories by Benjamin Taylor Hummon

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

Description

We exhibit a calculus of dot, string, and surface diagrams for describing computadic compositions. A surface diagram is a cube equipped with a stratification of regions, walls, seams, and nodes. We label the strata with morphisms in a strict 3-category C by codimension. Away from nodes, horizontal slice stratified squares are string diagrams representing compositions of 2-morphisms. In particular, a surface diagram has source and target string diagrams on its bottom and top faces, respectively. We may evaluate a surface diagram to give a 3-morphism in C. The domain and codomain are given by the evaluation of the source and target string diagrams. We build a 3-category Sd(C) of surface diagrams labeled by C in which composition is given by gluing along common faces. More generally, there is a 3-category Sd(G) of surface diagrams for any 3-computad G of generators. We characterize Sd(G) as the free 3-category on G. In Sd(G), diagrams are taken up to an isotopy-like relation called evolution. This relation destroys the braiding that we expect to have in a tricategory. We wish to capture braiding without working in the fully weak setting of a tricategory. We instead choose to work with in the semi-strict setting of Gray-categories. We define Gray surface diagrams to be those with certain good projection properties. Working up to an appropriate form of evolution, we construct the free Gray-category SdGray(G) of Gray-surface diagrams on a Gray-category. Last, we demonstrate the utility of surface diagrams by studying coherence relations for equivalence in a Gray-category. We show that the data encoding any incoherent equivalence may be recast as a coherent equivalence.

How long is Surface Diagrams for Gray-categories?

Surface Diagrams for Gray-categories by Benjamin Taylor Hummon is 132 pages long, and a total of 33,264 words.

This makes it 45% the length of the average book. It also has 41% more words than the average book.

How Long Does it Take to Read Surface Diagrams for Gray-categories Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 1 minute to read Surface Diagrams for Gray-categories aloud.

What Reading Level is Surface Diagrams for Gray-categories?

Surface Diagrams for Gray-categories is suitable for students ages 10 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 Surface Diagrams for Gray-categories?

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