Math 201 B Midterm 1
نویسنده
چکیده
Problem 1. Let C be a category with the zero object OC (that is, an object which is both universal and co-universal). In particular, for any pair of objects M and N , we have a distinguished morphism 0M,N ∈ HomC (M,N) , called the zero morphism, which is the composition of the unique morphisms M → OC and OC → N . Let M and N be objects in C and f ∈ HomC (M,N) . Recall that a kernel of f is a pair (K, k) where K is an object of C and k ∈ HomC (K,M) such that (a) f ◦ k = 0M,N ; (b) if (K ′, k′) is another pair with the same property, then there exists a unique h : K ′ → K such that k ◦ h = k′ (in other words, the pair (K, k) is a universal object in a suitable category). The dual concept is called a co-kernel of a morphism.
منابع مشابه
Early and midterm outcome after off-pump and on-pump surgery in Beating Heart Against Cardioplegic Arrest Studies (BHACAS 1 and 2): a pooled analysis of two randomised controlled trials.
BACKGROUND Although no randomised controlled trial has assessed the midterm effects of coronary-artery bypass surgery on the beating heart, this technique is being used in more and more patients. We did two randomised trials to compare the short-term morbidity associated with off-pump and on-pump myocardial revascularisation. Our aim was to pool the results to assess midterm outcomes. METHODS...
متن کاملMath 311: Complex Analysis — Automorphism Groups Lecture
Aut(C) = {analytic bijections f : C −→ C}. Any automorphism of the plane must be conformal, for if f ′(z) = 0 for some z then f takes the value f(z) with multiplicity n > 1, and so by the Local Mapping Theorem it is n-to-1 near z, impossible since f is an automorphism. By a problem on the midterm, we know the form of such automorphisms: they are f(z) = az + b, a, b ∈ C, a 6= 0. This description...
متن کاملOn m - regular systems on H ( 5 , q 2 )
The notion of m-regular system on the Hermitian variety H(n, q2) was introduced by B. Segre (Ann. Math. Pura Appl. 70:1–201, 1965). Here, three infinite families of hemisystems on H(5, q2), q odd, are constructed.
متن کاملMath 321: Real Variables Ii
Annoucements • Office = MATH 221 (Directly above the Mathematics Department Office.) • Email = [email protected] • Text = “Baby Rudin” – Principles of Mathematical Analysis 3/e by Walter Rudin • Course Website = “http://www.math.ubc.ca/∼feldman/m321/” • Topics: – Riemann-Stieltjes integral (§6) – Sequences & Series of functions (§7) – Power Series, Special Functions, Fourier Series (§8) – Ano...
متن کامل