11 citations · 24 across the 10 of their papers we have counts for
13 papers
Unifying Koszul dualities via point-set models
Dan Petersen, Victor Roca i Lucio, Sinan Yalin
The classical bar-cobar adjunction between dg algebras and dg coalgebras goes back to the origins of differential homological algebra as developed by Cartan, Eilenberg, Moore, and…
Point-set models for homotopy coherent coalgebras
Dan Petersen, Victor Roca i Lucio, Sinan Yalin
We show a first rectification result for homotopy chain coalgebras over a field. On the one hand, we consider the -category obtained by localizing differential graded coalg…
André-Quillen cohomology in the context of curved algebras
Joan Bellier-Millès, Sinan Yalin
The André-Quillen cohomology of an algebra with coefficients in a module is defined by deriving a functor based on Kähler differential forms. It can be computed using a cofibrant r…
Derived deformation theory of algebraic structures
Gregory Ginot, Sinan Yalin
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework vari…
Moduli spaces of (bi)algebra structures in topology and geometry
Sinan Yalin
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology,…
Deformation theory of bialgebras, higher Hochschild cohomology and formality
Gregory Ginot, Sinan Yalin
A first goal of this paper is to precisely relate the homotopy theories of bialgebras and -algebras. For this, we construct a conservative and fully faithful -functor…
Realization spaces of algebraic structures on cochains
Sinan Yalin
Given an algebraic structure on the homology of a chain complex, we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this st…
Function spaces and classifying spaces of algebras over a prop
Sinan Yalin
The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We…
Moduli stacks of algebraic structures and deformation theory
Sinan Yalin
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, map…
Maurer-Cartan spaces of filtered L-infinity algebras
Sinan Yalin
We study several homotopical and geometric properties of Maurer-Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras pl…
Simplicial localization of homotopy algebras over a prop
Sinan Yalin
We prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer-Kan equivalence between the simplicial localizations of the associated cat…
The homotopy theory of bialgebras over pairs of operads
Sinan Yalin
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a…
Classifying spaces of algebras over a prop
Sinan Yalin
We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop se…