A Cubical Approach to Synthetic Homotopy Theory in nLab
A Cubical Approach to Synthetic Homotopy Theory in nLab
In this paper, we describe a cubical approach to developing homotopy theory within type theory. The identity type is complemented with higher- ...
synthetic homotopy theory in nLab
Moreover, since the formal HoTT proof generalizes the traditional statement to more general (∞,1)-toposes, it is actually a genuine new ...
A Cubical Approach to Synthetic Homotopy Theory
Abstract—Homotopy theory can be developed synthetically in homotopy type theory, using types to describe spaces, the identity type to describe paths in a ...
Cubical type theory is a flavor of dependent type theory in which maps out of an interval primitive is used to define cubical path types.
homotopy type theory - references in nLab
A Cubical Approach to Synthetic Homotopy Theory. · A syntax for cubical type theory. · Implementation of Univalence in Cubical Sets, github · A ...
Often the “synthetic approach” is just referred to as “axiomatic”. For instance model categories were introduced as “axiomatic homotopy theory” ...
Stable homotopy type theory? - hopf algebras - MathOverflow
Heuristically, the starting point is the fact that in any category C with (Cartesian) products every object X has a unique comonoid structure, ...
A Synthetic Approach to Higher Equalities | The n-Category Café
3) We would like a foundations that is based on homotopy theory or categories/higher categories/groupoids/higher groupoids, in which homotopy ...
A type theory for synthetic ∞-categories - Emily Riehl
Our approach is based on the following idea, which was also suggested independently by Joyal. Homotopy type theory admits semantics not only in simplicial sets ...
cubical set - exposition in nLab
2. Cubical sets in homotopy theory · Eilenberg and Mac Lane proved a normalisation theorem which may be found in Mac Lane's book 'Homology'.
Motivation for the nLab's definition of cohomology?
It can also be described as trying to make higher homotopy theory look more like that of the fundamental group, and so nonabelian (in this book ...
Formalization of π₄(S³)≅ℤ/2ℤ in Cubical Agda completed
Furthermore, I expect there to be no problem to translate the proof to cartesian cubical type theory which can then be interpreted in spaces (using the ...
Homotopy type theory - Wikipedia
^ Univalence is a type, a property of the identity type IdU of a universe U —Martín Hötzel Escardó (2018) · ^ "Univalence is a type, and the univalence axiom ...
Categorification and the Cosmic Cube | The n-Category Café
interpolates between homological algebra and general simplicial homotopy theory. So with Dyckerhoff's paper we seem to be dipping down to the ...
nlab-scraper.ipynb · dmarx/nlab_feb24 at main - Hugging Face
... nlab/all_pages" def get_url(url): response = requests. ... A Cubical Approach to Synthetic Homotopy Theory ... model 338 A-n space 339 A-theory 340 A. Ch ...
Categorical homotopy theory Emily Riehl - Johns Hopkins University
For instance, it is well known that the homotopy category of a simplicial model category is enriched over the homotopy category of spaces.
Variations on a theme of homotopy - Numdam
Algebraic models for n-types are known and their homotopy theory as well. A final point is that this traditional approach to homotopy theory re- ally only ...
Equivariant stable homotopy theory and the Kervaire invariant ...
... approach to spectra. 460. 7.3. Stabilization and model structures ... the cubical diagram in C obtained by smashing the maps f, g and h ...
arXiv:2205.00386v3 [math.CT] 11 Mar 2024
The setting is Riehl–Shulman's synthetic (∞, 1)-category theory [62] which takes place in a simplicially augmented version of homotopy type ...
Evan Cavallo, Why some cubical models don't present spaces
Homotopy Type Theory Electronic Seminar Talks, 2024-03-28 https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html Historically, ...