Category Theory Lab
About: We are a group of mathematicians with an interest in category theory at CSU. We host talks on category theory and related fields (homotopy theory, higher categories, homological algebra). Our focus for Spring 2019 is to build a foundation on a wide variety of topics, enabling participants to find categorical concepts related to their research.
Meetings: Thursdays, 2:00pm, Engineering E105.
Organizers: Alex McCleary and Joshua Mirth.
Schedule of Talks
To volunteer for a talk, or make a topic request, please email the organizers.
Spring 2019
March 28 - Alex McCleary, "Simplicial Objects and the Dold-Kan Correspondence"
March 7 - Jānis Lazovskis
February 21 - John Bush, "Comma Categories"
February 7 - Joshua Mirth, "Simplicial Sets, Simplicial Complexes, and Geometric Realizations"
Fall 2018
August 28 - Alex McCleary, "A General Introduction to Category Theory"
September 4 - Alex McCleary, "Infinity Categories"
September 11 - Joshua Mirth, "Limits and Colimits"
September 18 - Amit Patel, "Localization"
September 25 - James Wilson, "From Abelian to Monoidal Categories"
October 2 - Vance Blankers, "Sheaves"
October 9 - Joshua Mirth, "Introduction to Derived Categories"
October 16 - Dustin Sauriol, "An Exploration of the Leray Spectral Sequence"
October 30 - Alex McCleary, "Introduction to Adjoint Functors"
November 6 - Alex McCleary, "Fibrations, Cofibrations, and Weak Equivalences"
November 13 - John Bush, "Ends and Coends"
Summer 2018
June 13 - Alex McCleary, "Kan Extensions"
June 20 - Joshua Mirth, "Simplicial Sets"
June 27 - Alex McCleary, "Quasi-Categories"
July 11 - Vance Blankers, "Moduli Problems"
July 18 - Alex McCleary, "Adjoint Functors"
July 25 - Joshua Mirth, "The Yoneda Lemma"
August 1 - Johnathan Bush, "Topoi and the Category of Sets"
August 8 - Dean Bisogno, "Projective Resolutions"
Recommended Resources
Basic Category Theory by Tom Leinster (a gentle introduction; just the basics)
Category Theory in Context by Emily Riehl (general introduction to category theory, at the level of beginning graduate student).
Categorical Homotopy Theory by Emily Riehl
Higher Algebra by Jacob Lurie
Higher Topos Theory by Jacob Lurie
nLab (wiki for all things category theory; somewhat infamous).
The n-Category Café (group blog on category theory, particularly higher category theory, and related topics).
Seven Sketches in Compositionality by Brendan Fong and David Spivak (unergraduate-level introduction to applied category theory).