Study of LY2886721 in Mild Cognitive Impairment Due to Alzheimer's Disease or Mild Alzheimer's Disease

Inclusion Criteria: Meets criteria for MCI due to AD or Mild AD All participants will be required to undergo assessment via the Mini Mental State Examination (MMSE) scale at screening * Participants with MMSE scores of 20 to 26, inclusive, may be enrolled provided they meet the criteria for mild AD, as follows: * Participant meets the National Institute of Neurological and Communicative Disorders and Stroke/Alzheimer's Disease and Related Disorders Association (NINCDS/ADRDA) criteria for probable AD * Clinical Dementia Rating Scale (CDR) score of 0.5 or 1 * Positive scan for the presence of amyloid beta * Participants with MMSE of 27 to 30, inclusive, may be enrolled as participants with MCI due to AD provided they meet the following criteria: * Gradual and progressive change in memory function as reported by the participant or a caregiver during a period of more than 6 months * Free and Cued Selective Reminding Test with Immediate Recall (FCSRT-IR): free recall ≤22 and total recall ≤46 * Absence of dementia * Preservation of functional independence * Exclusion of other potential (vascular, traumatic, or medical) causes of cognitive decline, where possible * Positive scan for the presence of amyloid beta * Women must be postmenopausal * Men are required to use an approved barrier method of contraception if their partners are pregnant, or of childbearing potential and not using approved contraceptive methods Exclusion Criteria: * Participant in another drug or device study * Have a history of frontotemporal dementia, Lewy body disease, vascular dementia, Huntington's disease, Parkinson's disease, progressive supranuclear palsy (PSNP), or other movement disorder * Participants are not on a stable standard of care (acetylcholinesterase inhibitors, memantine) initiated less than 2 months prior to entry or have less than 4 weeks of stable therapy. Note: Stable standard of care is allowed. * Have had a serious infectious disease affecting the brain in the past 5 years * Have had a serious or repeat head injury * Have significant retinal impairment or disease * Have had a stroke or other circulation problems that are affecting current health * Have had a seizure * Have major depressive disorder and are not on a stable dose of medication. Participants who no longer meet the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition-Text Revision (DSM-IV) criteria for major depression may be included * History of schizophrenia, bipolar disorder, or severe mental illness * History of alcohol or drug abuse * Have asthma, chronic obstructive pulmonary disease (COPD), or other breathing disease that is not controlled with medicine * Have human immunodeficiency virus (HIV) or syphilis * Are taking blood thinners