U+21A3 RIGHTWARDS ARROW WITH TAIL

U+21A3 was added to Unicode in version 1.1 (1993). It belongs to the block Arrows in the Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as z notation total injection.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. In text U+21A3 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The Wikipedia has the following information about this codepoint:

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence (aka bijective function), which uniquely maps all elements in both domain and codomain to each other, (see figures).

Occasionally, an injective function from X to Y is denoted f: XY, using an arrow with a barbed tail (U+21A3 ↣ rightwards arrow with tail). The set of injective functions from X to Y may be denoted YX using a notation derived from that used for falling factorial powers, since if X and Y are finite sets with respectively m and n elements, the number of injections from X to Y is nm (see the twelvefold way).

A function f that is not injective is sometimes called many-to-one. However, this terminology is also sometimes used to mean "single-valued", i.e., each argument is mapped to at most one value.

A monomorphism is a generalization of an injective function in category theory.

Representations

System Representation
8611
UTF-8 E2 86 A3
UTF-16 21 A3
UTF-32 00 00 21 A3
URL-Quoted %E2%86%A3
HTML-Escape ↣
Wrong windows-1252 Mojibake ↣
HTML-Escape ↣
HTML-Escape ↣
alias z notation total injection
LaTeX \rightarrowtail

Elsewhere

Complete Record

Property Value
Age (age) 1.1
Unicode Name (na) RIGHTWARDS ARROW WITH TAIL
Unicode 1 Name (na1) RIGHT ARROW WITH TAIL
Block (blk) Arrows
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) None
Decomposition Mapping (dm) ↣
Lowercase (Lower)
Simple Lowercase Mapping (slc) ↣
Lowercase Mapping (lc) ↣
Uppercase (Upper)
Simple Uppercase Mapping (suc) ↣
Uppercase Mapping (uc) ↣
Simple Titlecase Mapping (stc) ↣
Titlecase Mapping (tc) ↣
Case Folding (cf) ↣
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Bidi Paired Bracket (bpb) ↣
Bidi Paired Bracket Type (bpt) None
Cased (Cased)
Composition Exclusion (CE)
Case Ignorable (CI)
Full Composition Exclusion (Comp_Ex)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Dash (Dash)
Deprecated (Dep)
Default Ignorable Code Point (DI)
Diacritic (Dia)
East Asian Width (ea) Neutral
Extender (Ext)
FC NFKC Closure (FC_NFKC) ↣
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hangul Syllable Type (hst) Not Applicable
Hyphen (Hyphen)
ID Continue (IDC)
Ideographic (Ideo)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
InMC (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Join Control (Join_C)
Jamo Short Name (JSN)
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) ↣
NFKC Quick Check (NFKC_QC) Yes
NFKD Quick Check (NFKD_QC) Yes
Numeric Type (nt) None
Numeric Value (nv) NaN
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Radical (Radical)
Sentence Break (SB) Other
Simple Case Folding (scf) ↣
Script Extension (scx) Common
Soft Dotted (SD)
STerm (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)