We frequently use the language of
category theory
in algebraic topology. We should be aware of the fact
that the collection of all topological spaces does not
form a set. We also need more advanced set theory to
study
model categories
. We need
ordinals
and transﬁnite induction.
There is a ﬁeld called mathematical logic in
which people study logical structure themselves.
Category theory is used frequently. It seems that
model categories
are used in this ﬁeld these days.
