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Model structures and derived functors, minus homotopy

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If you have a question about this talk, please contact Guilherme Lima de Carvalho e Silva .

It is now understood that Quillen’s notion of ‘closed model category’ captures the essence of abstract homotopy theory very well; but at the same time, the requirement that model categories have all finite limits and colimits means that not every (∞, 1)-category can be presented by a model category. By relaxing this requirement, we are able to expand the class of model categories enough to include presentations for all (∞, 1)-categories. One curious feature of this development is the absence of homotopical concepts in the proofs: the basic theory is purely category-theoretic.

Examples in this talk will be drawn from classical homological algebra. Time permitting, we will see how Tor and Ext can be described as absolute Kan extensions.

This talk is part of the Junior Category Theory Seminar series.

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