Admit

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late Middle English: from Latin admittere, from ad- ‘to’ + mittere ‘send’.

wiktionary

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From Middle English admitten, amitten, borrowed from Old French admettre, amettre(“to admit”), from Latin admittō(“to allow entrance, inlet”, literally “to send to”), from ad- + mittere(“to send”).

etymonline

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admit (v.)

late 14c., "let in," from Latin admittere "admit, give entrance, allow to enter; grant an audience," of acts, "let be done, allow, permit," from ad "to" (see ad-) + mittere "let go, send" (see mission). Sense of "to concede in argument as valid or true" is first recorded early 15c. In Middle English sometimes also amit, after Old French amettre, which was refashioned 15c. Related: Admitted; Admitting.