  We investigate the categorical connection between Dialectica constructions,
Kolmogorov problems, Veloso problems and Blass problems. We show that the work
of Kolmogorov can be regarded as a bridge between Veloso's abstract notion of a
problem and the conceptual problems Blass discussed in his
questions-and-answers framework. This bridge can be seen by means of the
categorical Dialectica constructions introduced in de Paiva's dissertation and
reformulated by da Silva to account for set-theoretical foundational
assumptions. The use of categorical concepts allows us to provide several
examples, connecting extremely different areas of mathematics, and using simple
methods. This paper also shows that while Blass and Kolmogorov notions of
problem can be investigated using the Zermelo-Fraenkel (ZF) set-theoretical
framework, Veloso problems require the Axiom of Choice (AC). Moreover, weaker
notions of choice (dependent choice and countable choice) can also be accounted
for in the problems' framework.
