so suppose that we have a morphism m : x -> y of short exact sequences, and suppose that we consider the functor from short exact sequences to base objects given by "homs from x, modulo homs that extend to y" ... or something like that... ??then to what extent can we recover m from this functor??
we should also try to clear up the situation with stuff like "the doctrine with syntactic 2-category given by the concrete operations on the algebroid of finite-dimensional vector spaces over field k" or something like that... probably just comes down to mostly obvious concept of "abelian category with all objects semi-simple" (or something like that... then also "tensored" version and so forth), but good to clarify
(categorified) "equational" nature of such characterization...
No comments:
Post a Comment