  We study the uniform computational content of different versions of the Baire
Category Theorem in the Weihrauch lattice. The Baire Category Theorem can be
seen as a pigeonhole principle that states that a complete (i.e., "large")
metric space cannot be decomposed into countably many nowhere dense (i.e.,
"small") pieces. The Baire Category Theorem is an illuminating example of a
theorem that can be used to demonstrate that one classical theorem can have
several different computational interpretations. For one, we distinguish two
different logical versions of the theorem, where one can be seen as the
contrapositive form of the other one. The first version aims to find an
uncovered point in the space, given a sequence of nowhere dense closed sets.
The second version aims to find the index of a closed set that is somewhere
dense, given a sequence of closed sets that cover the space. Even though the
two statements behind these versions are equivalent to each other in classical
logic, they are not equivalent in intuitionistic logic and likewise they
exhibit different computational behavior in the Weihrauch lattice. Besides this
logical distinction, we also consider different ways how the sequence of closed
sets is "given". Essentially, we can distinguish between positive and negative
information on closed sets. We discuss all the four resulting versions of the
Baire Category Theorem. Somewhat surprisingly it turns out that the difference
in providing the input information can also be expressed with the jump
operation. Finally, we also relate the Baire Category Theorem to notions of
genericity and computably comeager sets.
