Mathematics for the non-mathematician

Foundations of Mathematics for the Working Mathematician

∞-Categories for the Working Mathematician

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition, product, pullback, retract, and limits of towers; see Lemma C.1.1. Proof. For now see [17, 11.1.4] and dualize. On account of the dual of Lemma C.1.1, any set of maps in a cocomplete category “cellularly g...

Burritos for the Hungry Mathematician

The advent of fast-casual Mexican-style dining establishments, such as Chipotle and Qdoba, has greatly improved the productivity of research mathematicians and theoretical computer scientists in recent years. Still, many experience confusion upon encountering burritos for the first time. Numerous burrito tutorials (of varying quality) are to be found on the Internet. Some describe a burrito as ...

0 Derived categories for the working mathematician

It is becoming increasingly difficult for geometers and even physicists to avoid papers containing phrases like “triangulated category”, not to mention derived functors. I will give some motivation for such things from algebraic geometry, and show how the concepts are already familiar from topology. This gives a natural and simple way to look at cohomology and other scary concepts in homologica...

The mathematician as a formalist