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⊣

left tack

Left Tack

⊣ has no single meaning across notation; its job depends on the system that uses it. It marks a relation in logic, a left adjunction in category theory, and a left-identity function in APL. A bare glyph needs its formula or notation system to be read correctly.

Text symbol

What ⊣ means

Read ⊣ through the notation that defines it.

In category theory, F ⊣ G says F is left adjoint to G—a formal relationship between two constructions. APL, a symbolic programming language, uses ⊣ as a left-identity function: X ⊣ Y returns X, while ⊣Y returns Y.

In logic, ⊣ is the reverse turnstile; the exact relation it marks depends on the system.

The direction changes the job

The history of the turnstile family starts in formal logic. Frege's 1879 book Begriffsschrift, a notation system for logic, used an assertion sign made from a horizontal content stroke and a vertical judgment stroke. Later logical systems developed related signs such as and for derivation and semantic consequence.

APL's history records two competing ways to name tack direction. Some compound APL names therefore do not align with Unicode's left/right names, even though the drawn sign is unchanged.

Technical notation: a bare ⊣ needs its formula or named system to give a dependable reading.

Don't swap it with or ; a reversed stroke or extra bar changes the sign.

What it means when someone sends it to you

3 readings

F is the left adjoint of G.

Don't confuse it with

⊢

Right Tack

Its upright stroke meets the horizontal bar at the opposite end, so it faces the other way from ⊣.

⊨

True

It has a double upright stroke; ⊣ has only one.

⊥

Up Tack

Its stem drops from a top bar; ⊣ has a sideways bar. The up tack is also used for bottom, falsity, or perpendicularity.

┤

Box Drawings Light Vertical And Left

Box-drawing piece for tables and frames; it may look like ⊣ but is not a logic sign.

Combination ideas

Functor F is left adjoint to functor G.

φ and ψ each prove the other.

APL: returns the left argument, 1.

Questions people ask

Is ⊣ the same as ?

No. They face opposite ways, and a formal system can assign them different roles; swapping them can change the statement.

How to type or find ⊣

Also called: reverse turnstile · dashv · left tee
Search it as: turnstile · APL left identity · category theory adjunction
Shows up in: Anything that takes text · its shape is whatever your font draws

Windows (Word)

⎇Alt+XType 22A3, then AltX to get ⊣.

Windows

⊞Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win .).

macOS

⌃Control+⌘Command+␣SpaceOpen the character viewer and search “left tack”.

Linux

⎈Ctrl+⇧Shift+UType 22a3, then Enter or Space.

HTML

⊣

CSS

\22A3

LaTeX

Use \dashv in math mode.

HTML

Use ⊣ or include the literal character ⊣.

Codes and encoding1 code points

HTML decimal

⊣

HTML hex

⊣

CSS content

content: "\22A3";

Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.

URL encoded

%E2%8A%A3

On screen

Code points

JS .length

UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

Maths & numbers1,835 symbols

1️⃣📏📐✖️➕➖➗🟰♾️#️⃣*️⃣0️⃣