Tagged Questions

For requesting, clarifying, and comparing definitions of mathematical terms.

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Is an étale morphism of algebraic stacks locally quasi-finite?

An étale morphism of schemes is unramified, and an unramified morphism is locally quasi-finite. Does the same hold for étale morphisms of algebraic stacks? Let us recall the definitions, following ...
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Understanding the roots of homomorphism and homeomorphism

I understand the formal (i.e. mathematical) definitions of the terms "homomorphism" and "homeomorphism" as they relate to functions, but I am curious as to the origin of these terms. I don't know ...
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Why do isotropic spaces deserve their name?

Wiki defines a quadratic form to be isotropic if it evaluates to zero at some vector. What does this have to do with isotropy in physics i.e uniformity in all directions? From my experience so far, ...
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Why so many 'multi-part' definitions, as opposed to 'unified' ones?

Many definitions consist of multiple parts: an equivalence relation is symmetric AND reflexive AND transitive; a topology is closed over finite intersections AND over arbitrary unions; etc. However, ...
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Why is cos at $\pi/2$ not undefined?

If the $\cos$ function is based off of the ratio of the adjacent side of Euclidean, right triangle, with fixed hypotenuse length (such as the unit circle), then how does this correspond to a defined ...
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Prove Limit Addition Thm as x approaches infinity

I am supposed to prove prove $\lim_{x\to \infty} [f(x)+g(x)]= L+M$. Starting to realize I don't really understand the formal definition of a limit, although I do understand the general concept. ...
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Anti-Diagonal Matrix

Hi just a quick question. Can a anti-diagonal have zero in its diagonal? I have this definition in my paper. "An anti-diagonal matrix is a square matrix where all the values are zeroes except those ...
What is $R$-algebra?
(To be clear, I mean a ring by a ring with unity.) Here is a definition in Wikipedia: Let $R$ be a commutative ring. Let $(M,+,\cdot)$ be an $R$-module. Let $\ast$ be a binary operation ...