Cockett received his Bachelor of Science from the University of Warwick in 1974,^[3] and earned his PhD from the University of Leeds in 1979 for his research in injectives and localizations in category theory, studying under Alfred Goldie.^[4]

Cockett has been a professor of computer science at the University of Calgary since 1991, previously holding the title of professor at the University of Tennessee.^[5][6]

Cockett works primarily in the fields of category theory, categorical programming, and quantum programming.^[3] Cockett is a member of the organizing committee for the Foundational Methods in Computer Science (FMCS) conference,^[3] an annual workshop for researchers in theoretical computer science and category theory supported by the Pacific Institute for the Mathematical Sciences (PIMS).^[7]

His most cited publications^[2] include:

• Weakly distributive categories^[8]
• Restriction categories I: categories of partial maps^[9]
• Differential categories^[10]
• Cartesian differential categories^[11]
• Differential structure, tangent structure, and SDG^[12]

Cockett has been married to fellow University of Calgary professor Polly Knowlton Cockett since 1984,^[13] they have three children together: Audrey Lane, Rowan, and Grayson.^[14] Cockett is an avid cross-country skier, taking part in the Canadian Birkebeiner on more than one occasion,^[15][16] as well as volunteering as an instructor.^[14]

Cockett and his wife have volunteered for numerous environmentally-focused initiatives, including as lecturers for the Calgary Parks Biodiversity Conservation program at Nose Hill Park,^[14] and with the Alberta Wilderness Association,^[14] where his family's work earned them an award from the city of Calgary.^[14]