Homotopy Structures for Algebras over a Monad Export

@article{citeulike:658900, author = {Grandis, Marco and Macdonald, John}, citeulike-article-id = {658900}, citeulike-linkout-0 = {http://dx.doi.org/10.1023/A:1008678719663}, comment = {If a category A has a homotopy theory defined via a cocylinder, then this paper shows how to exten this to the category of Eilenberg-Moore algebras for a monad on A. They manage to do this for symmetric monoidal categories, but not sure how far this can be pushed in the categorical setting. I suppose they do the symmetric monoidal case by virtue of the coherence theorem, which allows it to be viewed as algebras for a monad on Cat. May be interesting to look at extending this to 2-Monads on Cat. Also, does this extend to the Koslowski definition of polycategories as a bicategory of (moandic?) spans?}, doi = {10.1023/A:1008678719663}, journal = {Applied Categorical Structures}, keywords = {homotopy, monads}, number = {3}, pages = {227--260}, posted-at = {2006-05-20 13:10:52}, priority = {4}, title = {Homotopy Structures for Algebras over a Monad}, url = {http://dx.doi.org/10.1023/A:1008678719663}, volume = {7}, year = {1999} }

TY - JOUR ID - citeulike:658900 L3 - citeulike-article-id:658900 IS - 3 JF - Applied Categorical Structures EP - 260 TI - Homotopy Structures for Algebras over a Monad VL - 7 SP - 227 KW - homotopy KW - monads N1 - If a category A has a homotopy theory defined via a cocylinder, then this paper shows how to exten this to the category of Eilenberg-Moore algebras for a monad on A. They manage to do this for symmetric monoidal categories, but not sure how far this can be pushed in the categorical setting. I suppose they do the symmetric monoidal case by virtue of the coherence theorem, which allows it to be viewed as algebras for a monad on Cat. May be interesting to look at extending this to 2-Monads on Cat. Also, does this extend to the Koslowski definition of polycategories as a bicategory of (moandic?) spans? AU - Grandis, Marco AU - Macdonald, John PY - 1999/// UR - http://dx.doi.org/10.1023/A:1008678719663 ER -