Proto-exact categories and injective Banach modules
Jack Kelly
TL;DR
This paper develops the theory of covers and envelopes in proto-exact categories and applies it to establish the existence of enough injectives in categories of Banach modules over arbitrary Banach rings.
Contribution
It introduces the theory of covers and envelopes in proto-exact categories and proves the existence of enough injectives for Banach modules over any Banach ring.
Findings
Established the basic theory of covers and envelopes in proto-exact categories.
Proved the existence of enough injectives in categories of Banach modules over arbitrary Banach rings.
Extended the framework of proto-exact categories to functional analysis contexts.
Abstract
We develop the basic theory of covers and envelopes in proto-exact categories. As an application, we prove the existence of enough injectives for categories of Banach modules over arbitrary Banach rings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research · Rings, Modules, and Algebras