Bicategories of spans as cartesian bicategories
Stephen Lack, R.F.C. Walters, and R.J. Wood
TL;DR
This paper characterizes bicategories of spans as cartesian bicategories where every comonad has an Eilenberg-Moore object and all left adjoint arrows are comonadic, providing a structural insight.
Contribution
It offers a new characterization of bicategories of spans using properties of comonads and adjunctions within cartesian bicategories.
Findings
Bicategories of spans are identified as a special class of cartesian bicategories.
Every comonad in these bicategories has an Eilenberg-Moore object.
All left adjoint arrows are shown to be comonadic.
Abstract
Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg-Moore ob ject and every left adjoint arrow is comonadic.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras