http://www.numdam.org/item/CTGDC_2002__43_1_49_0.pdf WebWe will extend the definitions and techniques used to study schemes to algebraic spaces and algebraic stacks. We will give lots of motivation, examples, and applications. Topics will include Grothendieck topologies, descent, algebraic spaces, fibered categories, algebraic stacks, quotient stacks, deformation theory, torsors and gerbes.
Fibre product of objects in a category
WebWhat does fibered mean? Information and translations of fibered in the most comprehensive dictionary definitions resource on the web. Login . WebOct 24, 2024 · Crystals in fibered categories. In general, if E is a fibered category over F, then a crystal is a cartesian section of the fibered category. In the special case when F is the category of infinitesimal extensions of a scheme X and E the category of quasicoherent modules over objects of F, then crystals of this fibered category are the same as ... city of hamilton pool bylaw
quasicoherent sheaf in nLab
Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs) of objects such as vector bundles can be defined. As an example, for each … See more There are many examples in topology and geometry where some types of objects are considered to exist on or above or over some underlying base space. The classical examples include vector bundles, principal bundles, … See more Fibered categories 1. The functor $${\displaystyle {\text{Ob}}:{\textbf {Cat}}\to {\textbf {Set}}}$$, sending a category to its set of objects, is a … See more • Grothendieck construction • Stack (mathematics) • Artin's criterion • Fibration of simplicial sets See more There are two essentially equivalent technical definitions of fibred categories, both of which will be described below. All discussion in this section ignores the set-theoretical issues … See more The 2-categories of fibred categories and split categories The categories fibred over a fixed category $${\displaystyle E}$$ form a 2-category $${\displaystyle \mathbf {Fib} (E)}$$, where the category of morphisms between two fibred categories See more • SGA 1.VI - Fibered categories and descent - pages 119-153 • Grothendieck fibration at the nLab See more WebJan 28, 2005 · A Grothendieck fibration is a functor P : A → X which essentially allows you to divide the category A into subcategories A x called fibers over the objects x of X , with pullback functors between... don\u0027t feed the tulpa