Rigidification of algebras over essentially algebraic theories
J. Rosicky
TL;DR
This paper explores extending rigidification theorems from algebraic theories to finite limit theories and from simplicial sets to broader monoidal model categories, providing partial answers.
Contribution
It investigates the possibility of generalizing rigidification results to more complex theories and categories, expanding the scope of prior theorems.
Findings
Partial extension of rigidification to finite limit theories
Analysis of rigidification in broader monoidal model categories
Identification of conditions for successful rigidification
Abstract
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from algebraic theories to finite limit theories and from simplicial sets to more general monoidal model categories. We will present some answers to this question.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models