正品蓝导航

Geoffrey Cruttwell

Department Head; Associate Professor
Office
Dunn 211

Biography

I am an assistant professor in the Department of Mathematics and Computer Science at 正品蓝导航, an adjunct Professor at the Dalhousie university mathematics department, and a member of the Atlantic category theory group. I am interested in a wide variety of subjects related to category theory, such as:

  • Differential categories and tangent structures
  • Synthetic differential geometry

Publications

  1.  A simplicial foundation for differential and sector forms in tangent categories
    G.S.H. Cruttwell and Rory Lucyshyn-Wright. , 2018. 
  2.   Connections in tangent categories
    Robin Cockett and G.S.H. Cruttwell. , Vol. 32 (26), pg. 835-888, 2017
  3.  Differential bundles and fibrations for tangent categories
    Robin Cockett and G.S.H. Cruttwell. , Vol. LIX (1) pg. 10-92, 2018. .
  4.  The Jacobi identity for tangent categories.
    J.R.B. Cockett and G.S.H. Cruttwell. , Vol. LVI (4) pg. 301--316, 2015. 
  5. Cartesian differential categories revisited
    G.S.H. Cruttwell. , 22 pages, 2015. 
  6. Differential structure, tangent structure, and SDG
    J.R.B. Cockett and G.S.H. Cruttwell.  Vol. 22 (2), pg. 331-417, 2014. (This has been extensively updated to take into account an earlier paper of Rosicky's. For reference, here is the older version).
  7. Forms and exterior differentiation in Cartesian differential categories
    G.S.H. Cruttwell. , Vol. 28, pg. 981-1001, 2013. 
  8. Differential Restriction Categories
    J.R.B. Cockett, G.S.H. Cruttwell, and Jonathan Gallagher. , Vol. 25, pp 537-613, 2011. 
  9. A Unified Framework for Generalized Multicategories
    G.S.H. Cruttwell and Michael A. Shulman. , Vol. 24, pg. 580-655, 2010. 
  10. CCD lattices in Presheaf Categories
    G.S.H. Cruttwell, F. Marmolejo, and R.J. Wood. , Vol. 18, pg. 157-171, 2007. 
  11. Dimensions of Fractals in the Large
    M.R. Allen, G.S.H. Cruttwell, K. Hare, J.O. Ronning. , Volume 31 (1), pg. 5-13, 2007. 

 

Submissions and other works:

  1. Affine geometric spaces in tangent categories
    Rick Blute, G.S.H. Cruttwell, and Rory Lucyshyn-Wright. Submitted. 
  2. Combinatorial Game Categories
    J.R.B. Cockett, G.S.H. Cruttwell, and Kevin Saff. Under revision. PDF
  3. Normed Spaces and the Change of Base for Enriched Categories
    G.S.H. Cruttwell, PhD Thesis, Dalhousie University, 2008.  PDF
  4. A Study of CCD Lattices in a Functor Category
    G.S.H. Cruttwell, MSc Thesis, Dalhousie University, 2005. PDF

 

Talks:

  1.  Differential equations in tangent categories
    A talk given at , July 2017.
  2.  General connections in tangent categories
    A talk given at , June 2017.
  3.  A simplicial framework for de Rham cohomology in a tangent category
    A talk given at , August 2016
  4.    The Jacobi identity for tangent categories
    A talk given at , June 2015. 
  5. Bundles, pullbacks and fibrations for tangent categories
    A talk given at , June 2015.
  6. Counting finite categories
    An invited talk given at the  (special session on New Directions in Category Theory), October 2014. 
  7. Structures in tangent categories
    A talk given at , June 2014. 
  8. Introducing tangent categories and An alternative view of the tangent category axioms
    Talks given at , June 2014.
  9. Connections in tangent categories
    A talk given at the , October 2013. 
  10. Tangent categories, vector bundles, and connections
    A talk given in the  at Dalhousie University, September 2013.
  11. Differential categories and differential algebra
    An invited talk given at the , May 2013. 
  12. An introduction to categories
    A talk given to the Math and Computer Science Society of 正品蓝导航, March 2013. 
  13. Differential structure, tangent structure, and SDG
    A talk given at , June 2012. 
  14. Reconsidering Cartesian differential categories
    A talk given at , February 2012. 
  15. A tale of two tangent bundles
    A talk given at , October 2011. 
  16. Combining differential categories and manifolds
    An invited talk, given at , June 2011.
  17. Embeddings for atlas categories
    A talk given in the , March 2011. 
  18. Differential and tangent structure for restriction categories
    A talk given at , October 2010. 
  19. Combinatorial Game Categories
    A talk given at , June 2010. 
  20. Differential Restriction Categories II
    A talk given at . 
  21. A Unified Framework for Generalized Multicategories
    An invited talk given at , June 2010. 
  22. T-Monoids and 2-Dimensional Category Theory
    Notes for a series of talks given in the  on enriched categories, internal categories, 2-categories, and double categories, leading to the main construction in "A Unified Framework for Generalized Multicategories" (updated to December 9, 2009). 
  23. Combinatorial Game Categories
    A talk given at , November 2009. 
  24. A Unified Framework for Generalized Multicategories
    An invited talk given at , June 2009.
  25. Change of Base for Enriched Categories
    A talk given at , June 2008.
  26. Change of Base and the Amazing Technicolour Double Categories
    A talk given in the , June 2008.
  27. Change of Base for Enriched Categories
    A talk given in the , November 2007.
  28. Analysis and Enriched Category Theory
    Notes for my  talk, June 2007. 
  29. A Look At Some Classical Mathematical Structures
    A talk given in the Dalhousie Honours Mathematics Seminar, February 2007.
  30. Summing Cantor Sets: When Does 0+0=2?
    A talk given in the Dalhousie Honours Mathematics Seminar, November 2006.
  31. Normed and Ordered Algebraic Structures
    A talk given in the , October 2006.
  32. A Category of Games
    A talk given in the Dalhousie Game Theory Seminar, May 2006.
  33. A Generalization of Normed Linear Spaces
    A talk given in the , April 2006.
  34. CCD Lattices in a Functor Category
    A talk given in the , September 2005.
  35. A Category Theory View of Products
    A talk given in the , July 2005.
  36. Surreal Numbers
    A talk given in the University of Waterloo Short Attention Span Seminars, November 2003.

Teaching

正品蓝导航

  • Math/Comp 2211: Discrete Structures (Fall 2018)
  • Math 4111: Topology (Winter 2018)
  • Math 4951: Differential Categories (Winter 2018)
  • Comp 1731: Programming Techniques & Algorithms (Winter 2018)
  • Math 1151: Applied Calculus (Fall 2017)
  • Math 3111: Real Analysis I (Fall 2017)
  • Math 4951: Differential Categories I (Fall 2017)
  • Math 1111: Calculus I (Winter 2017)
  • Math 3031: History of Mathematics (Winter 2017)
  • Math 4221: Modern Algebra (Winter 2017)
  • Math 1151 : Applied Calculus (Fall 2015)
  • Math 3111 : Real Analysis (Fall 2015)
  • Math 1111: Calculus I (Winter 2015)
  • Math 3121: Real Analysis II (Winter 2015)
  • Math 3111: Real Analysis (Fall 2014)
  • Math 1151: Applied Calculus (Fall 2014)
  • Math 4111: Topology (Winter 2014)
  • Math 2221: Linear Algebra (Winter 2014)
  • Math 3111: Real Analysis (Fall 2013)
  • Math 1111: Calculus I (Fall 2013)
  • Math 4211: Modern Algebra II (Winter 2013)
  • Math 1111: Calculus I (Winter 2013)
  • Math 3111: Real Analysis (Fall 2012)

University of Calgary

  • CPSC 413: Design and Analysis of Algorithms (Fall 2010)
  • CPSC 513: Computability (Winter 2010)

Saint Mary's University

  • MGSC 1205: Introduction to Quantitative Methods I (Winter 2009)

Dalhousie University

  • Math 2002: Vector Calculus (July 28th - August 20th, 2008)
  • Math 1000: Calculus (July 4th - August 19th, 2007)

 

Research

Recent research news:

October 2014: Submitted paper: Differential bundles in tangent categories.

October 2014: Talk at the "New directions in category theory" special session of the AMS 2014 Eastern Sectional meeting: Counting Finite Categories.

June 2014: Talk at : on Structures in tangent categories.

June 2014: Two talks at : "Introducing tangent categories" and "An alternative view of the tangent category axioms".

October 2013: Submitted paper Tangent categories are locally Cartesian differential categories (with Robin Cockett).

October 2013: Talk at Union college math conference on Connections in tangent categories.

October 2013: New publication: Forms and exterior differentiation in Cartesian differential categories in Theory and Applications of Categories.

September 2013: Two-part talk in the @cat seminar on Tangent categories, vector bundles, and connections.