A Study of LY3002813 in Participants With Alzheimer's Disease

Inclusion Criteria: * Healthy Participants: * Overtly healthy males, as determined by medical history and physical examination, willing to use a reliable method of birth control and will not donate sperm during the study * Between 18 to 40 years old. * Body Mass Index (BMI) of between 18.0 and 30.0 kilogram per meter square (kg/m\^2), inclusive * Participants with Mild Cognitive Impairment Due to Alzheimer's Disease (AD) or AD: * Present with mild cognitive impairment (MCI) due to AD or mild-to-moderate AD * Men or nonfertile women, at least 50 years of age. Nonfertile is defined as hysterectomy and/or bilateral oophorectomy, or amenorrhea for at least 1 year * Have a caregiver/study informant who provides a separate written informed consent to participate * Have adequate vision and hearing for neuropsychological testing in the opinion of the investigator * Positive florbetapir scan Exclusion Criteria: -Healthy Participants: Have a history or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, immunological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data * Participants with Mild Cognitive Impairment Due to AD or AD: * Do not have a reliable caregiver/study informant who is in frequent contact with the participant, who will accompany the participant to the office and/or be available by telephone at designated times, and will monitor administration of prescribed medications * Are being monitored for radiation due to occupational exposure to ionized radiation, or exposure to ionizing radiation within last 12 months from an investigational study * History within the past 5 years of a primary or recurrent malignant disease with the exception of resected cutaneous squamous cell carcinoma in situ, basal cell carcinoma, cervical carcinoma in situ, or in situ prostate cancer with a normal prostate-specific antigen post resection * All Participants: * History of intracranial hemorrhage, cerebrovascular aneurysm or arteriovenous malformation, or carotid artery occlusion, or stroke or epilepsy * Have any contraindications for magnetic resonance imaging (MRI) studies, including claustrophobia, the presence of contraindicated metal (ferromagnetic) implants, cardiac pacemaker * Have allergies to humanized monoclonal antibodies, including proteins and diphenhydramine, epinephrine, and methylprednisolone * Have gamma globulin therapy within the last year * Previously dosed in any other study investigating active immunization against amyloid beta (Aβ) * Previously dosed in any other study investigating passive immunization against Aβ within the last 6 months