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- A Revisionist History of (Cisinski) Model Category
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- Home
- Our school
- Study with us
- Our research
-
Student life & resources
Postgraduate research
- Info for new students
- Current research students
- Postgraduate conference
- Postgraduate events
- Postgraduate student awards
- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
- Enrolment variation
- Changing tutorials
- Illness or misadventure
- Application form for existing casual tutors
- ARC grants Head of School sign off
- Computing facilities
- Choosing your major
- Engage with us
- News & events
- Contact
Abstract:
We'll begin with a revisionist history of model category theory (we'll imagine that, in place of homological algebra, the notion had its origin in category theory). Using this apocryphal premise, we'll describe Cisinski's theory of accessible localizers as the natural homotopification of the notion of models for a finite limit sketch in presheaf categories, a straightforward notion subsuming Grothendieck toposes, algebraic categories, and essentially algebraic categories.
We'll then use this understanding of model categories to revisit the 1963 work of Kan. While the study of categories, particularly here in Australia, has begotten the study of higher categories, e.g. 2,3,⋯,n,⋯,ω2,3,⋯,n,⋯,ω, in strict and various weak guises, little has been made of extending the structure down. We'll present a notion of ZZ-category, with zz-morphisms in all integer dimensions, and show that Kan's 1963 paper can be read as a proof that spectra admit presentation as locally finite pointed ZZ-groupoids.
Join this seminar via: https://unsw.zoom.us/j/99096430434
Zoom meeting ID: 990 9643 0434