Entanglement of Sections: The pushout of entangled and parameterized quantum information
H Sati, U Schreiber - arXiv preprint arXiv:2309.07245, 2023 - arxiv.org
Recently Freedman & Hastings asked for a mathematical theory that would unify quantum
entanglement/tensor-structure with parameterized/bundle-structure via their amalgamation …
entanglement/tensor-structure with parameterized/bundle-structure via their amalgamation …
An algebraic model for the free loop space
M Rivera - Higher Structures in Topology, Geometry, and Physics, 2024 - books.google.com
We describe an algebraic chain level construction that models the passage from an arbitrary
topological space to its free loop space. The input of the construction is a categorical …
topological space to its free loop space. The input of the construction is a categorical …
The category of necklaces is Reedy monoidal
VB Marques, A Mertens - arXiv preprint arXiv:2308.12796, 2023 - arxiv.org
In the first part of this note we further the study of the interactions between Reedy and
monoidal structures on a small category, building upon the work of Barwick. We define …
monoidal structures on a small category, building upon the work of Barwick. We define …
Szczarba's twisting cochain is comultiplicative
M Franz - arXiv preprint arXiv:2008.08943, 2020 - arxiv.org
We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map
from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the …
from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the …
The simplicial coalgebra of chains under three different notions of weak equivalence
G Raptis, M Rivera - International Mathematics Research …, 2024 - academic.oup.com
We study the simplicial coalgebra of chains on a simplicial set with respect to three notions
of weak equivalence. To this end, we construct three model structures on the category of …
of weak equivalence. To this end, we construct three model structures on the category of …
Hochschild and cyclic theory for categorical coalgebras: an algebraic model for the free loop space and its equivariant structure
D Tolosa - 2024 - search.proquest.com
We develop a cyclic theory for categorical coalgebras and show that, when applied to the
categorical coalgebra of singular chains on a space, this provides an algebraic model for its …
categorical coalgebra of singular chains on a space, this provides an algebraic model for its …
Cyclic homology of categorical coalgebras and the free loop space
M Rivera, D Tolosa - arXiv preprint arXiv:2403.08116, 2024 - arxiv.org
We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an
arbitrary topological space $ X $ is naturally quasi-isomorphic to the $ S^ 1$-equivariant …
arbitrary topological space $ X $ is naturally quasi-isomorphic to the $ S^ 1$-equivariant …
[PDF][PDF] Classifying space via homotopy coherent nerve
K Arakawa - arXiv preprint arXiv:2208.00550, 2022 - arxiv.org
Classifying Space via Homotopy Coherent Nerve Page 1 arXiv:2208.00550v3 [math.AT] 15
Feb 2023 CLASSIFYING SPACE VIA HOMOTOPY COHERENT NERVE KENSUKE ARAKAWA …
Feb 2023 CLASSIFYING SPACE VIA HOMOTOPY COHERENT NERVE KENSUKE ARAKAWA …
On BI-/HOPF Algebras and Their Applications to Renormalization Problems and Operadic Algebras
Y Mo - 2024 - search.proquest.com
In this thesis, we develop an algebraic framework for colored, colored connected, semi-
grouplike-flavored, and pathlike co-/bi-/Hopf algebras, which are essential in combinatorics …
grouplike-flavored, and pathlike co-/bi-/Hopf algebras, which are essential in combinatorics …
A detailed look at the Szczarba map
We explain how to derive an explicit formula for a natural transformation relating the (left
adjoints of) the homotopy coherent nerve and the Dwyer-Kan simplicial classifying space …
adjoints of) the homotopy coherent nerve and the Dwyer-Kan simplicial classifying space …