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Category TheoryIf f:A-->B is an equivalence in a category C and g:B-->A is a morphism such that gf=1_A (the identity on A) and fg=1_B, show that g is unique.
Prove that any two universal (initial) objects in a category C are equivalent.
Prove that any two couniversal (terminal) objects in a category C are equivalent.
In the category of abelian groups, show that the group A_1 x A_2 together with the homomorphisms f:A_1 --> A_1 x A_2, f(x)=(x,e) and g:A_2 --> A_1 x A_2, g(x)=(e,x) is a coproduct for {A_1,A_2}. Why is this not a coproduct in the category of groups?
Use a diagram to list the sample space showing possible arrangements of heads and tails when four coins are tossed . Then use the sample space to find the probability that:
Important information about Mathematics - Poisson Distribution, Metal plates are inspected regularly for flaws and average 2 flaws per square yard. Assume a Poisson process is applicable and calculate the probability of getting
Find the number of deer in the park
In planning for a major redesign, Beth collected data at her store on several consecutive Saturday mornings. She noticed that customers arrived at the checkout at a rate of approximately 100 per hour. Fully 20 percent of the customers had 10 items..
Application of calculus
Determine graphically using excel whether the equation could be possibly be an identity. If it can prove that it is. Here is an example of what I am working on at this time. Please explain how?
Use the formula to determine how long it takes the ball to return to the earth and Evaluate the maximum height of ball using given equation
Express logarithm into exponential form and solve logarithmic equation and solve the log 4 2 = 1/2 in exponential form.
What percentage of Americans earn below $20,000? What percenage of Americans earn above $ 43,000?
Information about "Poisson Distribution". During cross country pipeline construction, day production rates of more than 120 girth welds are not unusual. On pipe laying barges operating around the clock,
At Dot Com, a large retailer of popular books, demand is constant at 32,000 books per year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is $4 per book.
Probability: High Risk Apartments. In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants.
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