Monoidal algebraic model structures

Emily Riehl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Extending previous work, we define monoidal algebraic model structures and give examples. The main structural component is what we call an algebraic Quillen two-variable adjunction; the principal technical work is to develop the category theory necessary to characterize them. Our investigations reveal an important role played by "cellularity"-loosely, the property of a cofibration being a relative cell complex, not simply a retract of such-which we particularly emphasize. A main result is a simple criterion which shows that algebraic Quillen two-variable adjunctions correspond precisely to cell structures on the pushout-products of generating (trivial) cofibrations. As a corollary, we discover that the familiar monoidal model structures on categories and simplicial sets admit this extra algebraic structure.

Original languageEnglish
Pages (from-to)1069-1104
Number of pages36
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - Jun 2013
Externally publishedYes


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