Topology

This is the second of a three lecture course on equivariant homotopy theory from the Summer School on Homotopy Colimits, held at the University of Regina.

• Lecture 1
• Lecture 2
• Lecture 3

This is the third of a three lecture course on Homotopy theory of classifying spaces from the Summer School on Homotopy Colimits, held at the University of Regina.

• Lecture 1
• Lecture 2
• Lecture 3

This is the first of a three lecture course on Homotopy theory of classifying spaces from the Summer School on Homotopy Colimits, held at the University of Regina.

• Lecture 1
• Lecture 2
• Lecture 3

This is the second of a three lecture course on infinity categories from the Summer School on Homotopy Colimits, held at the University of Regina.

• Lecture 1
• Lecture 2
• Lecture 3

Higher algebraic K-theory is a powerful invariant which was originally defined for rings, but has since grown far beyond its initial scope to encompass increasingly rich and intricate settings. There are many different constructions of algebraic K-theory, reflecting the range of uses and perspectives encompassed by the theory. In this talk, I will describe a comparison between Waldhausen’s K-theory construction and Segal’s K-theory of symmetric monoidal categories. Precisely, given a symmetric monoidal category, we construct a Waldhausen category with an equivalent K-theory spectrum.