Home: go to the homepage U+2200 to U+22FF Mathematical Operators

# U+22A3Left Tack

U+22A3 was added in Unicode version 1.1 in 1993. It belongs to the block U+2200 to U+22FF 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 character is also known as reverse turnstile, non-theorem and does not yield.

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 mirrored into Right Tack. The word that U+22A3 forms with similar adjacent characters prevents a line break inside it.

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of "optimal solutions" to certain problems (i.e., constructions of objects having a certain universal property), such as the construction of a free group on a set in algebra, or the construction of the Stone–Čech compactification of a topological space in topology.

By definition, an adjunction between categories $C$ and $D$ is a pair of functors (assumed to be covariant)

$F:D\to C$   and   $G:C\to D$

and, for all objects $X$ in $C$ and $Y$ in $D$, a bijection between the respective morphism sets

${hom}_{C}\left(FY,X\right)\cong {hom}_{D}\left(Y,GX\right)$

such that this family of bijections is natural in $X$ and $Y$. Naturality here means that there are natural isomorphisms between the pair of functors $C\left(F-,X\right):D\to Se{t}^{\text{op}}$ and $D\left(-,GX\right):D\to Se{t}^{\text{op}}$ for a fixed $X$ in $C$, and also the pair of functors $C\left(FY,-\right):C\to Set$ and $D\left(Y,G-\right):C\to Set$ for a fixed $Y$ in $D$.

The functor $F$ is called a left adjoint functor or left adjoint to $G$, while $G$ is called a right adjoint functor or right adjoint to $F$. We write $F⊣G$.

An adjunction between categories $C$ and $D$ is somewhat akin to a "weak form" of an equivalence between $C$ and $D$, and indeed every equivalence is an adjunction. In many situations, an adjunction can be "upgraded" to an equivalence, by a suitable natural modification of the involved categories and functors.

## Representations

System Representation
8867
UTF-8 E2 8A A3
UTF-16 22 A3
UTF-32 00 00 22 A3
URL-Quoted %E2%8A%A3
HTML hex reference &#x22A3;
Wrong windows-1252 Mojibake âŠ£
HTML named entity &LeftTee;
HTML named entity &dashv;
alias reverse turnstile
alias non-theorem
alias does not yield
LATEX \dashv

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) LEFT TACK
Unicode 1 Name (na1)
Block (blk) Mathematical Operators
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) Left Tack
Lowercase (Lower)
Simple Lowercase Mapping (slc) Left Tack
Lowercase Mapping (lc) Left Tack
Uppercase (Upper)
Simple Uppercase Mapping (suc) Left Tack
Uppercase Mapping (uc) Left Tack
Simple Titlecase Mapping (stc) Left Tack
Titlecase Mapping (tc) Left Tack
Case Folding (cf) Left Tack
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) Left Tack
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) Left Tack
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Left Tack
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 Mirrored Glyph (bmg) Right Tack
Bidi Paired Bracket (bpb) Left Tack
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) Left Tack
Script Extension (scx)
Vertical Orientation (vo) R