Quotient Categories and Phases

Understand

We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object.

• Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'.
• We examine these and show that any suitable category with them arises as such a quotient of a category with coproducts.
• Motivation comes from projective geometry, and also quantum theory where they describe superpositions in the category of Hilbert spaces and continuous linear maps up to global phase.