### The category of cellular resolutions

Algebra and Geometry Seminar

12th June 2019, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

Cellular resolutions are a particular type of projective resolutions,

where the modules under consideration are associated with cell complexes and so

these resolutions also have combinatorial and topological information. Cellular

resolutions are a well-studied topic on the level of single resolutions and

certain specific families of cellular resolutions. One question coming out of

the work on families is to understand the structure of cellular resolutions

more generally. Our work has been constructing a category of cellular

resolutions and then looking at the classical category theoretical properties

and methods that have been very fruitful lately in the study of combinatorial

categories. Using these results we have shown that desirable properties

lift from topology to cellular resolutions, like homotopy colimits, and that

the ideas of representation stability can be applied to certain families of

cellular resolutions.

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