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# U+2A06N-Ary Square Union Operator

U+2A06 was added in Unicode version 3.2 in 2002. It belongs to the block U+2A00 to U+2AFF Supplemental Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+2A06 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with one other glyph.

In mathematics, the disjoint union (or discriminated union) $A\bigsqcup B$ of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.

A disjoint union of an indexed family of sets $\left({A}_{i}:i\in I\right)$ is a set $A,$ often denoted by $\underset{i\in I}{⨆}{A}_{i},$ with an injection of each ${A}_{i}$ into $A,$ such that the images of these injections form a partition of $A$ (that is, each element of $A$ belongs to exactly one of these images). A disjoint union of a family of pairwise disjoint sets is their union.

In category theory, the disjoint union is the coproduct of the category of sets, and thus defined up to a bijection. In this context, the notation $\coprod _{i\in I}{A}_{i}$ is often used.

The disjoint union of two sets $A$ and $B$ is written with infix notation as $A\bigsqcup B$. Some authors use the alternative notation $A\uplus B$ or $A\cup \phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}B$ (along with the corresponding $\underset{i\in I}{⨄}{A}_{i}$ or ${\bigcup \phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}}_{i\in I}{A}_{i}$).

A standard way for building the disjoint union is to define $A$ as the set of ordered pairs $\left(x,i\right)$ such that $x\in {A}_{i},$ and the injection ${A}_{i}\to A$ as $x↦\left(x,i\right).$

## Representations

System Representation
10758
UTF-8 E2 A8 86
UTF-16 2A 06
UTF-32 00 00 2A 06
URL-Quoted %E2%A8%86
HTML hex reference &#x2A06;
Wrong windows-1252 Mojibake â¨†
HTML named entity &bigsqcup;
HTML named entity &xsqcup;
LATEX \Elxsqcup

## Complete Record

Property Value
Age (age) 3.2 (2002)
Unicode Name (na) N-ARY SQUARE UNION OPERATOR
Unicode 1 Name (na1)
Block (blk) Supplemental Arrows-C
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) N-Ary Square Union Operator
Lowercase (Lower)
Simple Lowercase Mapping (slc) N-Ary Square Union Operator
Lowercase Mapping (lc) N-Ary Square Union Operator
Uppercase (Upper)
Simple Uppercase Mapping (suc) N-Ary Square Union Operator
Uppercase Mapping (uc) N-Ary Square Union Operator
Simple Titlecase Mapping (stc) N-Ary Square Union Operator
Titlecase Mapping (tc) N-Ary Square Union Operator
Case Folding (cf) N-Ary Square Union Operator
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
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)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) N-Ary Square Union Operator
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
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) N-Ary Square Union Operator
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) N-Ary Square Union Operator
NFKD Quick Check (NFKD_QC) Yes
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)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (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)
Bidi Paired Bracket (bpb) N-Ary Square Union Operator
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) N-Ary Square Union Operator
Script Extension (scx)
Vertical Orientation (vo) R