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, …

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 …

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 …

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

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 …

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 …

I don't know any thing about limits in 2-categories, but the definition of a pseudo 2-pullback looks like a homotopy pullback with truncated homotopy coherence conditions. This makes sense, …

Pullback of a $1$-form Ask Question Asked 12 years, 5 months ago Modified 12 years, 5 months ago

Apr 27, 2012 · Right, of course - it's been a long time since I've studied this stuff. It might make things clearer if you put some square brackets around the functions, to indicate that you're …

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).