Sometimes I wonder why people with so much knowledge of upper level mathematics get on Veeky Forums?
Category Theory
Ayden Bennett
Logan Lee
Maclane is still the best source for basic category theory. Some of the layer chapters should be supplemented with other material. The best way to learn category is to use it in other areas, I only really became comfortable with the basic machinery years after I became fluent in it, while picking up some simplicial homotopy theory. Homotopy theory in general is a good place to find examples of category theory. For example, coends play a crucial (sometimes left implicit) role in setting up smash products of spectra, or in "calculating" kan extensions, for instance in singularization/realization contexts.
Easton Mitchell
most of us grew up here
i've been here from age 13 to now doing graduate studies in math
you never really leave
Anthony Walker
>you never really leave
Save for you know the original bunch of tards that hang around here with us. Sites gone from a treehouse for retards with a specific sense of humour to a catch-all shithole.
Caleb Morales
How depressing :/
Landon Martin
hung*
Are you the dude I replied to?
Logan Nelson
>Are you the dude I replied to?
no
Alexander Phillips
>there is no foundations of math in pure category theory.
of course there is, for example
ncatlab.org
to name one.
Of course, just as people don't really need set theory for decades, nobody is really interested in those alternatives.
Matthew Turner
ETCS doesn't depend on category theory, people just express it in categorical language because it makes them happier.