An Introduction to Limits and Colimits | Category Theory Seminar | Pragalbh Kumar Awasthi

This talk is a part of the ISI Students' Category Theory Seminar. CT2604: An Introduction to Limits and Colimits Speaker: Pragalbh Kumar Awasthi (M.Math. 2nd year) The talk will be an introduction to the notions of limits and colimts in the context of category theory. We will see how these definitions capture the idea of universality in a general sense and unify various useful constructions known to us in familiar specific categories. We will see examples where existence of certain limits and colimits can imply nontrivial results about the category, and at the same time realizing an object X as a limit or colimit can give valuable information about X and F(X) or vice versa provided F preserves or reflects certain limits. The general content requires no prerequisites, but for some examples, a background in algebra and topology will be assumed.