WebIn any normal category with a zero object and kernels and cokernels for every morphism, the image of a morphism can be expressed as follows: im f = ker coker f In an abelian category (which is in particular binormal), if f is a monomorphism then f = ker coker f, and so f = im f . See also [ edit] Subobject Coimage Image (mathematics) Webde ned kernel and cokernel of a morphism f : X !Y in A. Let us copy the diagrams showing the universal property of kernels and cokernels from the last lecture: Ker(f) i X/ Y f / & =0 …

exact sequence in nLab

WebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … Web2.Every morphism f: X!Y has a kernel and a cokernel. 3.There is a zero object. 4.For every pair of objects X;Y, the product X Y exists. 5.Every monomorphism is the kernel of its cokernel, and every epimorphism is the cok-ernel of its kernel. Examples: The category of abelian groups forms an abelian category. The category R-mod forms an abelian ... chitwan valley

Commutative Algebra/Kernels, cokernels, products, coproducts

WebMore generally, the cokernel of a morphism f: X -> Y in some category (e.g. a homomorphism between groups or a bounded linear operator between Hilbert spaces) is an object Q and a morphism q: Y -> Q such that the composition q f is the zero morphism of the category, and furthermore q is universal with respect to this property. WebMore generally, the cokernel of a morphism f: X -> Y in some category (e.g. a homomorphism between groups or a bounded linear operator between Hilbert spaces) is … WebThe dual concept to that of kernel is that of cokernel. That is, the kernel of a morphism is its cokernel in the opposite category, and vice versa. As mentioned above, a kernel is a … grasshopper flying club