geometric type theory in nLab
1. Idea. Geometric type theory is a conjectural extension of geometric logic to an extensional dependent type theory. That is, it is supposed to ...
Contents · A geometric theory is a (possibly infinitary) first order theory whose models are preserved and reflected by geometric morphisms.
geometric homotopy type theory in nLab
Geometric type theory refers to a conjectural extension of geometric logic to an extensional dependent type theory that corresponds to sheaf toposes.
Type theory says that these fundamental rules are a calculus of terms, and that each term comes equipped with a type. Thus, the rules define one ...
Is there any work on Type Theory and Geometry? - ResearchGate
It is possible to produce logical type theories which are based on topology, such as homotopy type theory, but personally I think that as long ...
2. Related entries · geometric type theory, geometric homotopy type theory · synthetic geometry · differential geometry, differential topology, ...
nLab geometric functor · 1. Definition · 2. Related concepts. category · functor · internal logic · theory · hyperdoctrine · subobject poset ...
An infinitary coherent category or geometric category is a regular category in which the subobject posets Sub ( X ) Sub(X) have all small unions ...
Is nLab a good source? : r/math - Reddit
nLab presents category theory (and mathematics as a whole) from a ... geometry to provide motivation for categorical language. Upvote
What non-categorical applications are there of homotopical algebra?
In its homotopy category, the automorphism group of an object is exactly a commensurator, i.e. an isomorphism from one finite index subgroup to ...
What is the minimum required background to understand articles in ...
The nlab is a convenient (and probably the best) online reference for basic and advanced notions of category theory.
Journal Club -- Geometric Infinity-Function Theory -- Week 3
algebraically, one thinks of varieties with a structure sheaf not just of commutative rings but of (negatively graded) commutative dgas. This is ...
What is an $(\infty,1)$-topos, and why is this a good setting for doing ...
In this post on the n-Category Café, Urs Schreiber says that, "The theory of G-principal bundles makes sense in any (∞,1)-topos."
nLab -- General Discussion | The n-Category Café - Welcome
... geometry I, Topos theory. I am beginning to collect this stuff at n n Lab: derived ∞ \infty -stack. Posted by: Urs Schreiber on January 13 ...
theory of presheaf type in nLab
A geometric theory T \mathbb{T} is of presheaf type if its classifying topos Set [ T ] Set[\mathbb{T}] is equivalent to a presheaf topos.
... nLab would be more attractive for theory builders. People like ... Algebraic Geometry Algebraic Topology blog triumphalism Category Theory ...
Just a cautionary note - category theory has seemingly been at ...
(Obviously the Yoneda lemma is used in algebraic topology and geometry, but that's the odd one out on your list, and you don't really need categorical language ...
The nLab espouses the "n-point of view" (a deliberate pun on Wikipedia's "neutral point of view") that type theory, homotopy theory, category theory, and higher ...
Motivation for the nLab's definition of cohomology?
I am trying to penetrate the nLab article on cohomology. I don't know anything about higher category theory, but it seems like the real content ...
geometric function theory in nLab
More precisely, groupoidification in the sense of John Baez can be understood as geometric function theory for the case that collections of ...