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Results tagged with at.algebraic-topology
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user 14969
Homotopy theory, homological algebra, algebraic treatments of manifolds.
61
votes
8
answers
7k
views
Natural transformations as categorical homotopies
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 …
- 3,349
41
votes
Is Mac Lane still the best place to learn category theory?
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 …
29
votes
6
answers
4k
views
Concrete example of $\infty$-categories
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 …
- 3,349
4
votes
Natural transformations as categorical homotopies
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 …
- 3,349
2
votes
comparison between two monadic definitions for an operad
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 …
- 3,349