Homotopy Theory of linear coalgebras

2018/03/04 by Brice Le Grignou, Grignou, Brice Le, Damien Lejay +1
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1803.01376

openalex publication_date 2018/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example \mathcal E_∞-coalgebras, \mathcal A_∞-coalgebras, \mathcal L_∞-coalgebras etc. To do so, we define the category of complete curved algebras -- where the notion of quasi-isomorphims does not make sense -- and endow it with a model category structure, equivalent to that of the category of coalgebras.

Related

• Curved homotopy coalgebras
• Model structures for coalgebras
• The diagonal of cellular spaces and effective algebro-homotopical constructions
• The homotopy theory of coalgebras over simplicial comonads
• The category of E_∞-coalgebras, the E_∞-coalgebra structure on the homology, and the dimension completion of the fundamental group