Inclusion Criteria:

          -  Patients must have a histopathologically confirmed diagnosis of diffuse large B-cell
             lymphoma (DBLCL) or primary mediastinal large B-cell lymphoma

          -  Patients must have measurable disease, defined as at least one lesion that is >= 15 mm
             (>= 1.5 cm) in the longest axis on cross-sectional imaging and measurable in two
             perpendicular dimensions per spiral computed tomography (CT) scan or positron-emission
             tomography (PET)-CT scan

          -  Patients must have disease that is recurrent or refractory to standard therapy;
             patients must have failed front-line therapy and declined or are not candidates for
             autologous stem cell transplant (ASCT) or have failed prior ASCT

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2

          -  Life expectancy of greater than 12 weeks

          -  White blood cell (WBC) >= 2000/mm^3

          -  Absolute neutrophil count (ANC) >= 1000/mm^3

          -  Platelet count >= 100,000/mm^3

          -  Hemoglobin > 9.0 g/dL

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) (except patients with Gilbert
             syndrome, who can have total bilirubin < 3.0 mg/dL)

          -  Aspartate transaminase (AST) =< 2.5 x ULN

          -  Serum creatinine =< 2.0 mg/dL OR calculated creatinine clearance (CrCl) >= 30 mL/min
             (if using the Cockcroft-Gault formula)

          -  Negative urine or serum pregnancy test for females of child bearing potential within 7
             days prior to registration

               -  The effects of copanlisib and nivolumab on the developing human fetus are
                  unknown; for this reason, and because the study drugs used in this trial are
                  known to be teratogenic, females of child-bearing potential must agree to use
                  adequate contraception (hormonal or barrier method of birth control; abstinence)
                  prior to study entry, for the duration of study participation and for 5 months
                  after the last dose of study drug; males who are the sexual partners of a female
                  of child-bearing potential must use any contraceptive method with a failure rate
                  of less than 1% per year for the duration of study participation and for a period
                  of 7 months after the last dose of study drug; these periods of required use of
                  contraception have been calculated using the upper limit of the half-life for
                  nivolumab (25 days) and are based on the protocol requirement that females of
                  child-bearing potential use contraception for 5 months and males who are the
                  sexual partners of females of child-bearing potential use contraception for 7
                  months

               -  Females must not be breast-feeding for 1 month after last dose

               -  Females of child bearing potential must have a negative serum or urine pregnancy
                  test (minimum sensitivity 25 IU/L or equivalent units of human chorionic
                  gonadotropin [HCG]) within 24 hours prior to the start of nivolumab

               -  A female of child-bearing potential is defined as any female who has experienced
                  menarche and who has not undergone surgical sterilization (hysterectomy or
                  bilateral oophorectomy) or who is not postmenopausal; menopause is defined
                  clinically as 12 months of amenorrhea in a female over 45 in the absence of other
                  biological or physiological causes; in addition, females under the age of 55 must
                  have a documented serum follicle stimulating hormone (FSH) level less than 40
                  mIU/mL

               -  Females who are not of childbearing potential (i.e., who are postmenopausal or
                  surgically sterile) and azoospermic males do not require contraception

               -  Should a female of child-bearing potential become pregnant or suspect she is
                  pregnant while she or her partner is participating in this study, she (or the
                  participating partner) should inform the treating physician immediately

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Any high grade B-cell lymphoma

          -  Patients who have had chemotherapy within 2 weeks (6 weeks for nitrosoureas or
             mitomycin C), anticancer antibodies within 4 weeks, radio or toxin immunoconjugates
             within 2 weeks, radiation therapy within 3 weeks or major surgery within 2 weeks prior
             to entering the study

               -  Palliative (limited-field) radiation therapy is permitted if the patient has
                  additional measurable lesions to assess response of therapy

          -  Patients who have not recovered to grade 1 or less from any adverse events due to
             agents administered more than 4 weeks earlier (excluding alopecia)

          -  Patients who are receiving any other investigational agents

          -  Patients should be excluded if they have had prior treatment with a Pi3 kinase
             inhibitor, anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other
             antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint
             pathways; Note: Patients who previously received CART therapy and progressed will be
             eligible

          -  Patients who have received autologous stem cell transplant (ASCT) =< 8 weeks prior to
             the first dose of study drug or no adequate count recovery

          -  Patients with a prior history of allogeneic stem cell or solid organ transplantation

          -  Patients with evidence of active disease in the central nervous system (CNS) defined
             as either the presence of active lesions on magnetic resonance imaging (MRI) obtained
             within 4 weeks of registration or progressive neurological decline; patients with
             primary central nervous system (CNS) lymphoma who develop systemic recurrence
             following standard therapy may be included as long as no active CNS disease is present
             at the time or enrollment; similarly, patients with secondary involvement of the CNS
             from a systemic lymphoma may be included as long as the CNS disease has been optimally
             treated and they demonstrate no evidence of active CNS disease

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to copanlisib and/or nivolumab

          -  History of severe hypersensitivity reaction to any monoclonal antibody

          -  Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment
             of the investigator, would make the patient inappropriate for entry into this study or
             interfere significantly with the proper assessment of safety and toxicity of the
             prescribed regimens

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, non-healing wound or ulcer, or bone fracture, symptomatic congestive heart
             failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social
             situations that would limit compliance with study requirements

          -  Pregnant women are excluded from this study because copanlisib and nivolumab are
             agents with the potential for teratogenic or abortifacient effects; because there is
             an unknown but potential risk for adverse events in nursing infants secondary to
             treatment of the mother with copanlisib or nivolumab, breastfeeding should be
             discontinued for 1 month after last dose if the mother is treated with copanlisib or
             nivolumab

          -  Patients with human immunodeficiency virus (HIV):

               -  Patients with HIV are eligible for the study provided they meet the other
                  protocol criteria in addition to the following:

                    -  Undetectable HIV load by standard polymerase chain reaction (PCR) clinical
                       assay

                    -  Absolute CD4 count of >= 200 mm^3

                    -  Willing to maintain adherence to combination antiretroviral therapy

                    -  No history of acquired immunodeficiency syndrome (AIDS) defining condition
                       (other than lymphoma or CD4 cell count < 200 mm^3)

                    -  Likely to have near normal lifespan if not for the presence of
                       relapsed/refractory lymphoma

               -  The patients with evidence of hepatitis B virus (HBV) are eligible provided there
                  is minimal hepatic injury and the patient has undetectable HBV on suppressive HBV
                  therapy; patient must be willing to maintain adherence to HBV therapy

               -  Patients with previously treated and eradicated hepatitis C virus (HCV) who have
                  minimal hepatic injury are eligible

          -  Patients with active autoimmune disease or history of autoimmune disease that might
             recur, which may affect vital organ function or require immune suppressive treatment
             including systemic corticosteroids, should be excluded; these include but are not
             limited to patients with a history of immune related neurologic disease, multiple
             sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia
             gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE),
             connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's,
             ulcerative colitis, hepatitis; and patients with a history of toxic epidermal
             necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be
             excluded because of the risk of recurrence or exacerbation of disease; patients with
             vitiligo, endocrine deficiencies including thyroiditis managed with replacement
             hormones including physiologic corticosteroids are eligible; patients with rheumatoid
             arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with
             topical medication and patients with positive serology, such as antinuclear antibodies
             (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ
             involvement and potential need for systemic treatment but should otherwise be eligible

          -  Patients are permitted to enroll if they have vitiligo, type 1 diabetes mellitus,
             residual hypothyroidism due to autoimmune condition only requiring hormone
             replacement, psoriasis not requiring systemic treatment, or conditions not expected to
             recur in the absence of an external trigger (precipitating event); however, patients
             with uncontrolled type I or II diabetes mellitus will be excluded; uncontrolled
             diabetes is defined as hemoglobin A1c (HbA1c) > 8.5%

          -  Patients should be excluded if they have a condition requiring systemic treatment with
             either corticosteroids (> 10 mg daily prednisone equivalents) or other
             immunosuppressive medications within 14 days of study drug administration; inhaled or
             topical steroids and adrenal replacement doses =< 10 mg daily prednisone equivalents
             are permitted in the absence of active autoimmune disease; patients are permitted to
             use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids
             (with minimal systemic absorption); physiologic replacement doses of systemic
             corticosteroids are permitted, even if =< 10 mg/day prednisone equivalents; a brief
             course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for
             treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction
             caused by contact allergen) is permitted

          -  Patients who have had evidence of active or acute diverticulitis, intra-abdominal
             abscess, and gastrointestinal (GI) obstruction which are known risk factors for bowel
             perforation should be evaluated for the potential need for additional treatment before
             coming on study

          -  Patients with other active malignancy =< 3 years prior to registration for which
             active treatment is required must be excluded; patients with composite lymphomas that
             have a non-B-cell component must be excluded

               -  EXCEPTIONS: Non-melanotic skin cancers or carcinoma-in-situ of the cervix

          -  Copanlisib is primarily metabolized by CYP3A4; therefore, the concomitant use of
             strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin,
             ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g.
             rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) are not permitted
             from 14 days prior to enrollment until the end of the study

               -  Note: Because the lists of these agents are constantly changing, it is important
                  to regularly consult a frequently-updated medical reference; as part of the
                  enrollment/informed consent procedures, the patient will be counseled on the risk
                  of interactions with other agents, and what to do if new medications need to be
                  prescribed or if the patient is considering a new over-the-counter medicine or
                  herbal product; other medications that are prohibited while on copanlisib
                  treatment:

                    -  Herbal medications/preparations (except for vitamins)

                    -  Anti-arrhythmic therapy other than beta blockers or digoxin