homotopy type
The vertical unity of concepts in mathematics through the lens of homotopy type theory
... foundation, homotopy type theory, there should be many opportunities to explore its potential for concept ...formation. Type the- ories have a large array of ingredients, from type formation ...
15
Free higher groups in homotopy type theory
... (the type theory developed in the book [20]), and if the status of Question 2 was related to the status of semisimplicial ...The type theory that we consider in this paper is the standard homotopy ...
10
HoTT-Crypt : A Study in Homotopy Type Theory based on Cryptography
... inductive type representing a graphical model in a topological ...inductive type acts as an abstract model for the encoded cryptographic system and enables us to specify the correctness proper- ties as ...
16
Classification of Rational Homotopy Type for 8 Cohomological Dimension Elliptic Spaces
... rational homotopy types of manifolds are in general fascinating and various (see ...Rational Homotopy Theory; Elliptic Spaces; Classification; Rational Homotopy Type; Minimal Model of ...
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Extending homotopy type theory with strict equality
... unspecified type theory containing a “connective” for strict equality ...in homotopy type theory, and we show how the missing gap is filled by our strict ...
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Singular Cochains and rational Homotopy Type
... discuss homotopy categories. For any category C having a notion of homotopy between morphisms satisfying Lemma 27, we may construct the classical homotopy category H o C ...are homotopy ...
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Examples of Rational Toral Rank Complex
... There is a CW complex T X , which gives a rational homotopical classification of almost free toral actions on spaces in the rational homotopy type of X associated with rational toral ranks and also presents ...
9
COMPUTING BRAID GROUPS OF GRAPHS WITH APPLICATIONS TO ROBOT MOTION PLANNING
... Key words and phrases: graph, braid group, configuration space, fundamental group, homotopy type, deformation retraction, collision free motion, planning algorithm, complexity, robotics.[r] ...
22
Localization Theory in an Infinity Topos
... In Chapter 2, we follow [Lur09] and [GK17] to give an overview of the theory of local classes of maps in an ∞-topos E . A class S of maps in E is said to be local (Definition 2.1.2) if it is closed under coproducts, ...
137
Arrangements of Submanifolds and the Tangent Bundle Complement
... Using the Nerve lemma we show that M (A) has the homotopy type of a finite simplicial complex. We generalize the classical theorem of Salvetti [73, Theorem 1] for hyperplane arrangements and show that this ...
163
Khovanov homotopy types and the Dold-Thom functor
... Khovanov homotopy type is a way of associating a (stable) space to each link L so that the classical invariants of the space yield the Khovanov homology of ...Khovanov homotopy types, using different ...
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The homotopy theory of Khovanov homology
... the homotopy category: deforming the input data up to homotopy may not result in the same homotopy ...of homotopy limits and homotopy colimits, which are now standard constructions in ...
36
Impact of Homotopy Theory
... Homotopy type theory is another branch of arithmetic that joins parts of a few extraordinary fields in a very surprising ...between homotopy hypothesis what's more, sort hypothesis. Homotopy ...
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Mapping spaces, configuration spaces and gauge theory
... the homotopy type of the associated space of connections modulo based gauge equivalence only depends on the rank of the intersection form and its signature (up to sign) modulo eight, ...different ...
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Fixed Points of Maps of a Nonaspherical Wedge
... the homotopy type of the wedge X P ∨ ...the homotopy type of a map of X and the Nielsen number is a homotopy type invariant, we will assume that we are concerned only with maps ...
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A Synopsis of Morphoid Type Theory
... Both Homotopy type theory (HoTT) and mor- phoid type theory (MTT) are intended as type- theoretic foundations for mathematics supporting a concept of ...L¨of type the- ory (Martin-L¨of, ...
12
Homotopy-initial algebras in type theory
... the type of natural numbers, by means of standard category-theoretic universal ...between type theory, homotopy theory and higher-dimensional category theory [4, 5, 12, 19, 23], which are at the core ...
42
Introduction – from type theory and homotopy theory to univalent foundations
... A second group of papers, which includes the papers by Barras, Coquand and Huber; by van den Berg and Moerdijk; by van Oosten; and by Shulman, is concerned with the investigation of models of type theories. Very ...
6
On Relative Homotopy Groups of Modules
... developed homotopy theory in module theory, parallel to the existing homotopy theory in ...unlike homotopy theory in topology, there are two types of homotopy theory in module theory, the ...
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A Nontrivial Product in the Stable Homotopy of Spheres
... To determine the stable homotopy groups of spheres is one of the most important problems in algebraic topology. So far, several methods have been found to determine the stable homotopy groups of spheres. ...
6