Memorial University of Newfoundland

 

 

Atlantic Association for Research in the Mathematical Sciences

CRG "Groups, Rings, Lie and Hopf Algebras"

Atlantic Algebra Centre

 

Tensor Topology

 

 

Mini course by Chris Heunen

University of Edinburgh

November 16 - 25, 2021

 

 

 

Tensor topology recognises that any monoidal category comes with a built-in notion of space, that can be cleanly separated from the other, nonspatial, aspects of the category, and studies the interaction between this space and the monoidal category, in the form of notions of support.

Lecture 1 will recall monoidal categories, braidings, the graphical calculus, and discuss the (Drinfeld) centre of a monoidal category.

Lecture 2 will revolve around the crucial notion of a central idempotent in a monoidal category. We will introduce the notion, build up basic results, and discuss examples.

Lecture 3 will deal with locales, or pointless topological spaces, and consider how the central idempotents in a monoidal category interact with locales.

Lecture 4 will recall the notion of sheaf, and prove the main theorem that any monoidal category is equivalent to the global sections of a sheaf of local monoidal categories.

Time permitting, we may also discuss localisable monads on monoidal categories or the relationship between monoidal categories and restriction categories.

The course will be suitable for undergraduates, graduate students, postdocs, faculty, and anyone interested in algebra. Due to the current situation caused by the corona virus disease, the mini course will take place virtually from 12:00 to 13:00 Newfoundland Standard Time at the following dates:

Lecture 1: Tuesday, November 16

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Lecture 2: Thursday, November 18

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Lecture 3: Tuesday, November 23

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Lecture 4: Thursday, November 25

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The mini course is jointly organised by the AARMS Collaborative Research Group “Groups, Rings, Lie and Hopf Algebras” and the Atlantic Algebra Centre. For further information, please contact Yorck Sommerhäuser at sommerh@mun.ca.

Literature:

“Tensor topology”, http://www.arxiv.org/abs/1810.01383
“Sheaf representation of monoidal categories”, http://www.arxiv.org/abs/2106.08896
“Space in monoidal categories”, http://arxiv.org/abs/1704.08086
“Localisable monads”, https://arxiv.org/abs/2108.01756
“Tensor restriction categories”, http://www.arxiv.org/abs/2009.12432