third abstract

Author: cangiuli

_posts/fl24/2024-11-01-angiuli.markdown

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+---
+layout:  post
+title:   "Indexed Families in Category Theory, Part II"
+authors: "Carlo Angiuli"
+date:    2024-10-25 14:00:00
+categories: Angiuli Fall2024
+---
+
+## Time and Location
+
+* **Date:** Friday, November 1
+* **Time:** 2:00-3:00 PM
+* **Location:** Luddy Hall 4111
+
+## Abstract
+
+This is the third in a series of lectures introducing how the language of
+category theory captures "dependency." In this lecture, we will continue our
+discussion of pullbacks, analyzing their relationship to fibers and base change.
+
+In this lecture series we will start with set-indexed families of sets,
+generalize from Set to arbitrary categories, and conclude with category-indexed
+families of categories. Topics covered will include bundles and sections, slice
+categories, pullbacks, base change, and Grothendieck fibrations.
+
+The categorical prerequisites are minimal: I will assume you know about
+categories, functors, terminal objects, and binary products. Knowledge of
+dependent type theory is not necessary but may provide additional motivation.
+If you already know what a Grothendieck fibration is, you probably won't learn
+anything new.
+
+By the end of this series, you will be prepared to understand the categorical
+semantics of dependent type theory (such as comprehension categories, display
+map categories, and categories with families / natural models), the categorical
+gluing approach to logical relations, and why everyone loves pullbacks so much.