Definition of pullback. - Mathematics Stack Exchange Concerning the difference between the pull-back of a vector field (page 134 of Guillemin and Pollack) and the pull-back of a differential form (page of 163 Guillemin and Pollack)
How to calculate the pullback of a $k$-form explicitly 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 wikipedia, pushforward for further details
terminology - What is the intuition behind pushouts and pullbacks in . . . E g , the set of solutions to any equation in two unknowns, such as $3x + 2 = y$, is obtained by pullback; Relations are essentially spans and then relation composition is given by pullback; characteristic predicate for sets make certain squares pullback, and that condition is used to specify characteristic arrows and truth-objects in general
Pullback in the category of graphs - Mathematics Stack Exchange Pullbacks form intersections of subobjects That is, the pullback [above] is obtained by forming the ‘intersection’ [loosely, as discussed below] of vertices, and keeping whatever edges that are in the intersection
understanding how to define pullback of differential forms After a bit of back and forth in the comments I have decided to write an extended discussion here The coordinate free way to describe the pull back of forms is to think of it as the dual to the differential
Intuition about pullbacks in differential geometry Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
What is a pullback of a metric, and how does it work? This post is over 4 years old by now, so I'm guessing the OP has moved on with their life But seeing as this post was the first result when I googled "pullback metric", and it has amassed over 8k views, I figure an answer may still be useful to someone else
Pullbacks commute with the exterior derivative I am trying to show by induction that pullbacks and the exterior derivative commute I know that this question has been discussed on this site, eg here and here However, none of these questions e
category theory - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers