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Horizontal & vertical categorification: from monoids to bicategories

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Categorification refers to the process of generalising a mathematical structure by considering it as a special case in a much richer setting. Horizontal categorification provides extra structure by considering a structure as a single object in a category; whereas vertical categorification takes a definition and replaces the sets with categories, the functions with functors, and so on. We will explore these two concepts in relation to a prototypical example: the monoid. In the process, we will develop two useful categorical structures: the monoidal category and the bicategory.

This talk is part of the Logic & Semantics for Dummies series.

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