"Math is not all about numbers. I do not do any numbers in my research as a category theorist."
"Category theory is the modern language that mathematicians use today."
"Did you know that language, that bridge itself, is built from mathematics? And that mathematics has a name, that's category theory."
"Category theory provides a language to help you identify when two things are really the same."
"The real power of category theory is being able to isolate the kind of property you care about."
"The non-bureaucratic aspect of category theory is that I can define things in a category, I can distill it to abstract things and then I can transfer them over to other categories."
"Sometimes some people, including me, like to say that category theory is the mathematics of mathematics."
"Really applying this category Theory to deep learning is one part of what category Theory does but once you start thinking about this, all things start looking like category Theory."
"Category theory gives us a bird's eye view of these things; all of these structures are categories."
"Category theory tells you that if you're interested in the variables, you're also interested in the kinds of things those variables are."
"...the metaphor like you said makes the morphism the fundamental thing rather than the objects I think that's huge because that's one of the deepest lessons about category theory is focusing on processes adding things."
"Isomorphisms in category Set are bijections."
"A covariant functor preserves the direction of arrows."
"An object like this does not always exist in every category. Right some categories it does. In others it doesn't. In set, it is a singleton set."
"It is indeed a category, it has identity arrows and it's associative."
"A monad is a monoid in the category of endofunctors."
"We want to understand what it means to preserve structure, and nothing defines it better than a functor. It's a functor that not only maps objects but also maps the connections between objects, which are morphisms or arrows."
"The coproduct is also a bi-functor, it takes two types and produces..."
"If you take any object in a category and any path to the terminal object, in every category, you can replace it with a singular path."
"The construction of natural number objects in category theory is remarkably simple yet powerful."
"Understanding categorical products and exponential objects helps us grasp the essence of category theory."
"In category theory we have to say and so team composed with T is usually written simply as T Square."
"Thank you so much for being here. I'm so happy that I can share my passion with you guys."
"The Yoneda Lemma is one of the most useful results in category theory for calculations but it also has very broad philosophical implications."
"I think it's a really nice idea because it means that if you understand what an adjoint functor is, then you can kind of understand how lots of different things in category theory are related to each other."
"The product functor is the right adjoint to the diagonal functor."
"Category theory unifies all these things and because of that, it's extremely useful when you want to lift yourself above the everyday programming chores."
"We need to be searching for ways of decomposing and recomposing solutions, and category theory is just like this wonderful reservoir of ideas about composing and decomposing things."
"The philosophy of category theory was we are more interested in mappings between things than in things themselves."
"Next time you think about morphisms and shapes, think about functors and categories."
"Can we build a category in which objects themselves are categories and arrows between them are functors?"
"In this category called 'cat', categories are objects and functors are morphisms."
"Isomorphism is the right notion of sameness, it's a bit weaker than equality, but it's what happens in categories."
"In a category, not every two pair of functions can be composed; they have to match end to end."
"If it's a category, what do we need? We need identity and composition."
"Category theory has inherently this global approach to everything."
"At the heart of 20th century mathematics lies one particular notion, and that's a notion of a category."
"A category with one object only is exactly the same thing as a monoid."
"When you were like two and you learned that some numbers are bigger than others, you were really doing category theory."
"A functor is like an upgraded version of a function because your things now are not just objects but they come with these arrows too."
"One of the beautiful things of category theory is its rigidity."
"Category theory is like a mathematical language for processes and how processes compose."