Coalgebra morphisms subsume open maps

Coalgebra Morphisms Subsume Open Maps

Coalgebra-to-Algebra Morphisms

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

Deformations of Coalgebra Morphisms

An algebraic deformation theory of coalgebra morphisms is constructed.

Morphisms of open games

We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category i...

The Geometry of Harmonic Maps and Morphisms

We give a survey of harmonic morphisms between Riemannian manifolds, concentrating on their construction and relations with the geometry of foliations.