![]() ![]() A section of a trivial bundle is just a function $U \to F$. A trivial bundle with fiber $F$ looks like the projection map $U \times F \to U$. To your third question, I think the observation that $\Gamma(-,Y)$ forms a sheaf on $X$ gives a nice context in which to think of sections $X$ to $Y$: they "live in" the sheaf $\Gamma(-,Y)$ as its globally defined elements.īundles are usually defined as being locally trival thingamajigs. More unfortunate is the annoying coincidence that when dealing with schemes the projection map from the espace étalé happens to be an étale morphism, because it is locally on its domain an isomorphism of schemes, a much stronger condition.$\Big)$ This is unfortunate, because the espace étalé has very little to with with étale cohomology. However, the French word "étalé" means "spread out", whereas "étale" (without the second accent) means "calm", and they were not intended to be used interchangeably in mathematics. $\Big($ Unfortunate linguistic warning: Many people incorrectly use the term "étale space". This explains the otherwise bizarre tradition of writing $\Gamma(U,F)$ instead of the the more compact notation $F(U)$. $\Gamma(-,Y)$ actually forms a sheaf of sets on $X$.Ĭonversely, given any sheaf of sets $F$ on a space $X$, one can form its espace étalé, a topological space over $X$, say $\pi: \acutet(F))$. maps $U\to Y$ such that the composition $U \to Y\to X$ is the identity (thus necessarily landing back in $U$). For $U\subseteq X$ open, the notation $\Gamma(U,Y)$ denotes sections of the map $\pi$ over $U$, i.e. The word "over" is used to activate the tradition of suppressing reference to the map $\pi$ and refering instead to the domain $Y$. Say $\pi: Y\to X$ is a space over $X$ (intentionaly vague). To your second question, I generally take the "right-inverse" or "pre-inverse" definition from category theory, because it relates back to others in the following precise way: Thus locally a section just looks like a function with codomain $T$, which is often required to be nice. $U\subset X$) isomorphic to some product $U\times T$, then we can locally identify the fibres with $T$. If one is talking about locally free / locally trivial bundles, meaning $E$ is locally (over open sets at each point $x\in X$, it takes value in the fibre (This is a fairly selective use of the word "function" which used to confuse me.) A section $\gamma$ of a (some-kind-of) bundle $E\to X$ is thought of as a "generalized function" on $X$ by thinking of it as a funcion with "varying codomain", i.e. Given the time it takes to create an individual sketch for each plane, this would be an ideal candidate for some iLogic/VB.Net automation.To your first question, "function on a space" $X$ usually means a morphism from $X$ to one of several "ground spaces" of choice, for example the reals if you work with smooth manifolds, Spec(A) if you work with schemes over a ring, etc. I admit – it's a slightly cumbersome work around. ![]() Then we can simply right click on any sketch line, and create a section view.ĥ) Hey presto – section views linked to work plane positions. And unfortunately, we can only have one line per sketch, AND we need to sketch a (non projected) line on top of the projected line, as projected lines cannot be referenced for the section line.ģ) Now we can create a drawing view, and 'Get Model Sketches' by right clicking on the assembly in the browser:Ĥ) The sketch lines should then be visible. So how do we do that?ġ) Get the required workplanes in the assembly model (if they are not already there).Ģ) Now we need the get the line of each plane into its own sketch, to be used later in the drawing. And the use of model sketches is the best one I've got so far. If you agree with me that this would be useful, add a Kudos vote to the thread.īut until this is included in the software, we need a workaround. ![]() There is an Ideastation request for this function here: Why do we need a model plane when we can simply reference any model edge I hear you ask? Well there may be occasions – particularly for our Inventor Construction crossover users (designing curtain walling, roofing, scaffolding, facias etc) where there is no model geometry on a gridline that you need to reference in a drawing view. Strangely, Inventor 2014 does not allow assembly or part planes to be projected into a drawing view sketch, so that they can be used to define a section line position. You want to create section views in an Inventor drawing, and have these be linked to work geometry (ideally a workplane) in the model file. ![]()
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