Geoffrey Cruttwell
Assistant professor, Math & Computer Science
Contact Information
- gcruttwell@mta.ca
- Phone
- (506) 364-2533
- Office
- Dunn 211
- Office hours
- Other websites
I am an assistant professor in the Department of Mathematics and Computer Science at Mount Allison University, 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
Constructions of the real numbers
Generalized multicategories
Double categories
Teaching
Mount Allison University
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 interests
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 Category theory 2014: on Structures in tangent categories.
June 2014: Two talks at FMCS 2014: "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.
Publications
Publications:
- A simplicial foundation for differential and sector forms in tangent categories
G.S.H. Cruttwell and Rory Lucyshyn-Wright. Journal of Homotopy and Related Structures, 2018. - Connections in tangent categories
Robin Cockett and G.S.H. Cruttwell. Theory and Applications of Categories, Vol. 32 (26), pg. 835-888, 2017 - Differential bundles and fibrations for tangent categories
Robin Cockett and G.S.H. Cruttwell. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Vol. LIX (1) pg. 10-92, 2018. . - The Jacobi identity for tangent categories.
J.R.B. Cockett and G.S.H. Cruttwell. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Vol. LVI (4) pg. 301--316, 2015. - Cartesian differential categories revisited
G.S.H. Cruttwell. Mathematical Structures in Computer Science, 22 pages, 2015. - Differential structure, tangent structure, and SDG
J.R.B. Cockett and G.S.H. Cruttwell. Applied Categorical Structures 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). - Forms and exterior differentiation in Cartesian differential categories
G.S.H. Cruttwell. Theory and Applications of Categories, Vol. 28, pg. 981-1001, 2013. - Differential Restriction Categories
J.R.B. Cockett, G.S.H. Cruttwell, and Jonathan Gallagher. Theory and Applications of Categories, Vol. 25, pp 537-613, 2011. - A Unified Framework for Generalized Multicategories
G.S.H. Cruttwell and Michael A. Shulman. Theory and Applications of Categories, Vol. 24, pg. 580-655, 2010. - CCD lattices in Presheaf Categories
G.S.H. Cruttwell, F. Marmolejo, and R.J. Wood. Theory and Applications of Categories, Vol. 18, pg. 157-171, 2007. - Dimensions of Fractals in the Large
M.R. Allen, G.S.H. Cruttwell, K. Hare, J.O. Ronning. Chaos, Solitons, and Fractals, Volume 31 (1), pg. 5-13, 2007.
Submissions and other works:
- Affine geometric spaces in tangent categories
Rick Blute, G.S.H. Cruttwell, and Rory Lucyshyn-Wright. Submitted. PDF - Combinatorial Game Categories
J.R.B. Cockett, G.S.H. Cruttwell, and Kevin Saff. Under revision. PDF - Normed Spaces and the Change of Base for Enriched Categories
G.S.H. Cruttwell, PhD Thesis, Dalhousie University, 2008. PDF - A Study of CCD Lattices in a Functor Category
G.S.H. Cruttwell, MSc Thesis, Dalhousie University, 2005. PDF
Talks:
- Differential equations in tangent categories
A talk given at Category Theory 2017, July 2017. - General connections in tangent categories
A talk given at FMCS 2017, June 2017. - A simplicial framework for de Rham cohomology in a tangent category
A talk given at Category theory 2016, August 2016 - The Jacobi identity for tangent categories
A talk given at Category theory 2015, June 2015. - Bundles, pullbacks and fibrations for tangent categories
A talk given at Foundational methods in computer science 23, June 2015. - Counting finite categories
An invited talk given at the Fall 2014 AMS Eastern Sectional meeting (special session on New Directions in Category Theory), October 2014. - Structures in tangent categories
A talk given at Category theory 2014, June 2014. - Introducing tangent categories and An alternative view of the tangent category axioms
Talks given at FMCS 2014, June 2014. - Connections in tangent categories
A talk given at the Union college math conference, October 2013. - Tangent categories, vector bundles, and connections
A talk given in the @cat seminar at Dalhousie University, September 2013. - Differential categories and differential algebra
An invited talk given at the Annual North American meeting of the ASL, May 2013. - An introduction to categories
A talk given to the Math and Computer Science Society of Mount Allison University, March 2013. - Differential structure, tangent structure, and SDG
A talk given at Foundational Methods in Computer Science 2012, June 2012. - Reconsidering Cartesian differential categories
A talk given at Logic and Interactions 2012 (Quantative approaches session), February 2012. - A tale of two tangent bundles
A talk given at Category theory Octobefest 2011, October 2011. - Combining differential categories and manifolds
An invited talk, given at Foundational Methods in Computer Science 2011, June 2011. - Embeddings for atlas categories
A talk given in the Calgary Peripatetic Seminar in Logic and Category Theory, March 2011. - Differential and tangent structure for restriction categories
A talk given at Octoberfest 2010, October 2010. - Combinatorial Game Categories
A talk given at Category Theory 2010, June 2010. - Differential Restriction Categories II
A talk given at FMCS, June 2010. - A Unified Framework for Generalized Multicategories
An invited talk given at CMS 2010 Summer Meeting (Tensor categories session) , June 2010. - T-Monoids and 2-Dimensional Category Theory
Notes for a series of talks given in the Calgary Peripatetic Seminar in Logic and Category Theory 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). - Combinatorial Game Categories
A talk given at Novemberfest 2009, November 2009. - A Unified Framework for Generalized Multicategories
An invited talk given at CT2009, June 2009. - Change of Base for Enriched Categories
A talk given at CT2008, June 2008. - Change of Base and the Amazing Technicolour Double Categories
A talk given in the Atlantic Category Theory Seminar, June 2008. - Change of Base for Enriched Categories
A talk given in the Atlantic Category Theory Seminar, November 2007. - Analysis and Enriched Category Theory
Notes for my CT2007 talk, June 2007. - A Look At Some Classical Mathematical Structures
A talk given in the Dalhousie Honours Mathematics Seminar, February 2007. - Summing Cantor Sets: When Does 0+0=2?
A talk given in the Dalhousie Honours Mathematics Seminar, November 2006. - Normed and Ordered Algebraic Structures
A talk given in the Atlantic Category Theory Seminar, October 2006. - A Category of Games
A talk given in the Dalhousie Game Theory Seminar, May 2006. - A Generalization of Normed Linear Spaces
A talk given in the Atlantic Category Theory Seminar, April 2006. - CCD Lattices in a Functor Category
A talk given in the Atlantic Category Theory Seminar, September 2005. - A Category Theory View of Products
A talk given in the Dalhousie Mathematics and Statistics Graduate Student Seminar, July 2005. - Surreal Numbers
A talk given in the University of Waterloo Short Attention Span Seminars, November 2003.