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nLab
nLab
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Contents
Purpose
The nLab records and explores a wide range of mathematics, physics, and philosophy. Along with work of an expository nature, original material can be found in abundance, as ca...
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site in nLab
Remark
Often a site is required to be a small category. But also large sites play a role.
Remark
Every coverage induces a Grothendieck topology. Often sites are defined to be categories equipped with ...
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locale in nLab
A
locale is, intuitively, like a topological space that may or may not have enough points (or even any points at all). It contains things we call open subspaces but there may or may not be enough poi...
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class in nLab
Internal classes
It is possible to internalize the notion of class inside of the foundations itself. Classes are either primitive, such as in class theory, or a derived concept from a notion of univer...
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local system in nLab
local system of coefficients for cohomology – is a system of coefficients for twisted cohomology.
Often this is presented or taken to be presented by a locally constant sheaf. Then cohomology with coe...
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adjoint functor in nLab
1
L
=
R^\dagger
\;\colon\;
\mathscr{H}_2 \leftrightarrows \mathscr{H}_1
\;\;\;\;\;\;\;\;\;\;\;
\text{means}
\;\;\;\;\;\;\;\;\;\;\;
\bigl\langle
L(-),\, -
\bigr\rangle_...