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, …

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 …

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 …

Dec 16, 2022 · understanding how to define pullback of differential forms Ask Question Asked 3 years ago Modified 2 years, 11 months 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 …

The role of the pullback to integration is that it allows us to lift integration defined in Rn up to the manifold (provided we have the partition of unity to weave things together). Essentially the …

CAVEAT: we can always pullback differential forms, but only pushforward vectors (and not vector fields, unless $\alpha$ is a diffeomorphism (which is obviously not the case here)). See …

Nov 9, 2011 · 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 …

May 30, 2012 · The pullback property for the big square (or rectangle) really follows from the pullback properties of the two small squares. Hint: Start with the right hand square.

Mar 6, 2021 · How is the pullback of a Riemannian metric defined? Ask Question Asked 4 years, 9 months ago Modified 4 years, 5 months ago