Engineering↗
Abelian Categories
Additive and abelian categories, the axioms, exactness in a general abelian category, the Freyd-Mitchell embedding theorem, and the standard examples.
Tag
Categories & Functors
Every page in the KEVOS library tagged Categories & Functors. 8 pages.
Engineering↗
Adjoint Functors
Adjoint pairs, unit and counit, the tensor-hom adjunction, preservation of limits and colimits, and the exactness consequences that make adjointness central to homological algebra.
Engineering↗
Categories and Morphisms
Categories, objects and morphisms, monomorphisms and epimorphisms defined by cancellation, isomorphisms, and why the arrow-theoretic definitions differ from the element-based ones.
Engineering↗
Duality and Opposite Categories
The opposite category, the duality principle, dual pairs of notions in homological algebra, and the limits of formal duality.
Engineering↗
Functors and Their Exactness Properties
Covariant and contravariant functors, composition, additive functors, faithful and full functors, and the exactness hierarchy that governs derived functors.
Engineering↗
Natural Transformations
Natural transformations and naturality squares, natural isomorphisms, functor categories, and the role of naturality in the long exact sequences.
Engineering↗
Products, Coproducts and Universal Constructions
Universal properties, products and coproducts in a general category, initial and terminal objects, and uniqueness up to unique isomorphism.
Engineering↗
Pullbacks, Pushouts and General Limits
Pullbacks and pushouts, their construction in module categories, limits and colimits over a diagram, and exactness of filtered colimits.
Related
Other tags in the library.
mathematics 387
abstract algebra 252
Machine Design 184
business 179
project management 158
Computational Number Theory 123
algebra handbook 85
graduate mathematics 85
handbook 79
templates and examples 78
History of Engineering 77
Manufacturing 76
algebra and trigonometry 74
universal algebra 62
algebra 60
project delivery 60
principles of project management 58
advanced algebra 53
Fasteners and Joints 53
Civil Engineering 48
CAD 42
Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
Power Transmission 34
template 34
Operational Excellence 32
example 31
project leadership 31
project teams 31
strategy 31
Business Expansion 29
Metrology 29
project management research 29
Sales & Marketing 29
personal development 27
behaviour change 26
habits 26
systems 26