Irreducible binary-biproduct maps between finite string modules #
This file specializes the generic binary-biproduct irreducibility criterion to literal finite string modules. Morphisms between two nonisomorphic string modules are categorical-radical, so two irreducible boundary maps with a common endpoint assemble to an irreducible map whenever their other endpoints are nonisomorphic.
Every morphism between two nonisomorphic finite string modules is categorically radical.
Two irreducible maps from one finite string module to nonisomorphic finite string modules assemble to an irreducible map into their binary biproduct.
Two irreducible maps from nonisomorphic finite string modules to one finite string module assemble to an irreducible map out of their binary biproduct.
Two maps from one finite string module to the same finite string module assemble to an irreducible binary lift when all scalar row operations on the second map remain irreducible.
The symmetric repeated-target criterion, with scalar row operations based at the second component.
Two maps from the same finite string module to one finite string module assemble to an irreducible binary desc when all scalar column operations on the second map remain irreducible.
The symmetric repeated-source criterion, with scalar column operations based at the second component.
The repeated-target criterion for two isomorphic, rather than literally equal, finite string-module summands.
The repeated-source criterion for two isomorphic, rather than literally equal, finite string-module summands.
The symmetric isomorphic-source criterion, based at the second component and transported through the opposite equality direction.