What does “control of a deformation problem” mean?

Is the expression “control of a deformation problem’ ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it ever defined? Answer AttributionSource : Link , Question Author : Jim Stasheff , Answer Author : Community

When are descriptions of formal unramifiedness/smoothness via lifting properties equivalent to those via induced arrows to pullbacks?

Formal unramifiedness of an arrow f:M→N in algebraic geometry or synthetic differential geometry in defined by asking the lifting problem below to have at most one solution (existence is not required). 1⟶M↓↗↓D⟶N In SDG, I think formal unramifiedness can also defined by asking the induced arrow TM→P to the pullback below to be a monomorphism. … Read more

Issue with “definition” of pseudo algebraically closed fields

I’m having an issue with a sentence in Chapter 11 of Fried & Jarden’s Field Arithmetic. As a “motto” for pseudo algebraically closed (PAC) fields, they say they are fields K such that “each nonempty variety defined over K has a K-rational point”. No mention of absolute irreducibility is made at this point. My issue … Read more

Dualizing complex definition ubiquity

The following definition is the one, I found here http://stacks.math.columbia.edu/tag/0A7A. But let me recall it (out of consistency’s sake): Definition For A a Noetherian ring, a dualizing complex for it is a complex of A-modules say ω∙A with the following properties 1.) ω∙A has finite injective dimension. 2.) Hi(ω∙A), is a finite A-modules for all … Read more

On the definition of ‘smooth vectors’ in Rieffel’s “Deformation Quantization for Actions of $ \mathbb{R}^{d} $”.

On the first page of Chapter 1 of Rieffel’s Deformation Quantization for Actions of $ \mathbb{R}^{d} $, Rieffel defines a family of seminorms on the space $ A^{\infty} $ of smooth vectors of a Fréchet space $ A $, for some action $ \alpha $ of the Lie group $ \mathbb{R}^{d} $ on $ A … Read more

On 2-actions of strict 2-groupoids?

I’m looking for an opinion if the following makes sense. A linear representation of a groupoid G is a functor ∇:G⟶VectK, where VectK is the category of vector spaces over K. I presume we could define analogously a linear 2-representation of a strict 2-grupoid 2–G as a strict 2-functor: 2–∇:2–G⟶2–VectK, where 2–VectK is the 2-category … Read more

Group presentation in the category of finite group

Context: I’m trying to deal with presentations in the framework of Gonthier et al. formalization of the group theory in the proof assistant Coq. It was used to machine check the Feit-Thompson odd order theorem. In this formalisation, all groups are assumed to be finite and it would be a lot of work to remove … Read more