$T$-forms and their properties

This paper continues the paper “Bilinear forms on categories” by the second of the authors. A class of nondegenerate forms is introduced; in particular, any isomorphism of a totally isotropic direct summand onto another totally isotropic direct summand of an object with a form this class can be extended till a metric automorphism of the object (even if the division by 2 of morpisms is impossible).