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Talk, University of Ottawa Colloquium

March 12, 2021 @ 3:00 pm - 4:00 pm

Associativity, Commutativity and Units: a Higher-dimensional ballet

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Associativity, commutativity and unit laws are axioms we typically learn about early on, in the context of numbers. We might then take them for granted until we meet non-commutative situations, such as multiplication of matrices, or symmetry groups. In higher dimensions we start to encounter non-associativity and non-unitality as well, but there is more nuance: rather than associativity simply being true or not true, there are shades of grey, where associativity holds up to isomorphism, equivalence, or just some sort of map. In this talk I will describe how those familiar three families of axioms become the essence of all the interesting features of weak higher-dimensional category theory. Moreover, rather than being three different types of axioms they are inextricably related via a higher-dimensional version of distributivity. The ballet they present is one of ebb and flow, give and take, where rigidity for one “dancer” always needs to be offset by flexibility in another. I will show that the apparently mundane maths of high school has deep category theoretical insights embedded in it, if we care to look. I will not assume any prior knowledge of category theory, but prior interest in pure mathematics will help.

The talk will be by Zoom, with links sent to anyone who registers.

Click here to register.


March 12, 2021
3:00 pm - 4:00 pm
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