Stabilité et homologie de factorisation équivariante

Autor: Miladinovic, Aleksandar

The aim of this thesis is to contribute to the study of the equivariant homotopy theory. Itconsists of three parts.In the first part we prove that the stabilization of the infinity category of G-spaces with respect tothe representation spheres is equ

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od_______166::d0fdee7f757e474662816fe2d8384449
https://theses.hal.science/tel-03920859

Théories à types dépendants et algèbre de dimension supérieure

Autor: Leena Subramaniam, Chaitanya

Publikováno v: Category Theory [math.CT]. Université de Paris, 2021. English

The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary monads on certa

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::35fbba14c93d5644c403f8f38aa60981
https://tel.archives-ouvertes.fr/tel-03369103/document

Computational descriptions of higher categories

Autor: Forest, Simon

Publikováno v: Category Theory [math.CT]. Institut Polytechnique de Paris, 2021. English. ⟨NNT : 2021IPPAX003⟩

Higher categories are algebraic structures consisting of cells of various dimensions equipped with notions of composition, which have found many applications in mathematics (algebraic topology in particular) and theoretical computer science. They are

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od_______212::6afda602fc833d15911aa353de3bd213
https://tel.archives-ouvertes.fr/tel-03155192

Catégories faibles et structures supérieures afférentes en théorie des types

Autor: Benjamin, Thibaut

Publikováno v: Formal Languages and Automata Theory [cs.FL]. Institut Polytechnique de Paris, 2020. English. ⟨NNT : 2020IPPAX077⟩

We study a type theoretic definition of weak omega-categories originally introduced by Finster and Mimram, inspired both from ideas coming from homotopy type theory and from a definition of weak omega-category due to Grothendieck and Maltsiniotis. Th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od______2592::42e29af0e28d739514d689a299e60b65
https://tel.archives-ouvertes.fr/tel-03106197/file/94836_BENJAMIN_2020_archivage.pdf

Cubical categories for homotopy and rewriting

Autor: Lucas, Maxime

Publikováno v: Algebraic Topology [math.AT]. Université Paris 7, Sorbonne Paris Cité, 2017. English
Algebraic Topology [math.AT]. Université Paris 7, Sorbonne Paris Cité, 2017. English. ⟨NNT : ⟩

Higher dimensional rewriting theory was born following work by Squier on the word problem in the 80s. The goal of this work is to extend and modernize those results from Squier. In the first part of this work we show how to use rewriting to prove coh

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::13e1a8a39695ffa6afce2c1d648e7bd4
https://hal.archives-ouvertes.fr/tel-01668359/document