Doubly weak double categories

Abstract: Double categories are a two-dimensional categorical structure with two different classes of 1-cells, and 2-cells shaped like a square. It is easy to define double categories with strict composition like 2-categories; but double categories with weak composition analogous to bicategories, for both kinds of 1-cells, are surprisingly difficult to define. We give a simple definition of "doubly weak double categories" by using the notion of "implicit" categorical structure, in which composition is not an algebraic operation at all but is witnessed by isomorphisms. Then we discuss various ways in which this can be made algebraic. This is joint work with Aaron David Fairbanks.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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