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I've seen many different notions of $\infty$-categories: actually I've seen the operadic-globular ones of Batanin and Leinster, and the opetopic, and eventually I'll see the simplicial ones too. Altho …

Well the two monads are quite different: in May definition you deal with an actual monad in $\mathbf {Cat}$ (i.e. a strict-$2$-category) while in the second case you work with monads in the bicategory …

Following the previous indication of Professor Brown I want to add another possible way to see natural transformation which is a generalization of the previous definition. Given categories $\mathc …

Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute. There is another possible d …

I doubt that someone could learn higher category theory (and more in general higher dimensional algebra) without first studying a little of category theory, mostly because the definition given in such …