Jul 28, 2020 · Consider the category of (undirected) multigraphs (possibly with loops) and multigraph homomorphisms. What are pullbacks in such a category? Is there an informal, colloquial and intuitive …

Aug 4, 2020 · What is the intuition behind pullbacks and pushouts? For example I know that for terminal objects kind of end a category, they are kind of last is some sense, and that a product is a kind of …

The term "metric" is familiar, but not the idea of a pullback on it. I have tried to find intuitive, beginner-friendly explanations of this concept without success. Your attempts would be appreciat...

Dec 16, 2022 · understanding how to define pullback of differential forms Ask Question Asked 3 years ago Modified 3 years ago

commutes. Moreover, the pullback $ (P, p_1, p_2)$ must be universal with respect to this diagram. Also, is it possible to define pushforward/pushout in terms of composition of functions? Thanks and regards!

The role of the pullback to integration is that it allows us to lift integration defined in $\mathbb {R}^n$ up to the manifold (provided we have the partition of unity to weave things together).

Take 8 objects, and form a cube, with all arrows directed towards the back-right-bottom corner. Suppose the back, top, bottom, left, and right faces are pullback squares. Show the front is also a pullback …

Aug 8, 2023 · Question about pullback and pushforward of sheaves Ask Question Asked 2 years, 5 months ago Modified 2 years, 4 months ago

I'm having trouble doing actual computations of the pullback of a k k -form. I know that a given differentiable map α: Rm → Rn α: R m → R n induces a map α∗: Ωk(Rn) → Ωk(Rm) α ∗: Ω k (R n) → …

May 30, 2015 · The change of variables theorem in multivariable calculus is a higher-dimensional, slightly less-elementary example of a pullback, used every time you convert a Cartesian integral to …